Curriculum Vitæ of Robert I. Soare December 5, 2013 Contents 1 Address 3 2 Short Biography 3 3 Educational Record 4 4 Professional Record 4 4.1 Editorial Duty: .......................... 5 4.2 Honorary Societies: ........................ 5 4.3 Professional Societies: ....................... 5 5 Grants 5 6 Honors and Recognition 5 7 Invited Addresses at Leading Congresses 6 8 Other Selected Invited Addresses 7 9 New PhD’s Whom Soare Brought to Chicago 9 10 Ph.D. Students Whom Soare Supervised: 10 11 Books 12 12 Publications in Elite Journals 13 1
Department of MathematicsUniversity of Chicago5734 University AvenueChicago, IL 60637(773) 702-6029e-mail: [email protected]
2 Short Biography
Robert Irving Soare was born in Orange, New Jersey, and graduated fromNewark Academy in 1959. At Princeton from 1959 to 1963, he studied math-ematical logic and computability theory with Alonzo Church and wrote a se-nior thesis with Church and his associate. He studied logic and computabilityat Cornell from 1963 to 1967 and wrote a Ph.D. thesis wth Anil Nerode in1967. From 1967 to 1973 he rose from Assistant Professor to full profes-sor of mathematics at the University of Illinois at Chicago (UIC). In 1974 hemoved across town to the University o Chicago as a professor of mathematics,a position he has held since then.
In 1983 he was appointed founding Chairman of the new Department ofComputer Sciece by the University President Hanna Gray. In 1994 PresicentSonnenschein named Soare the Paul Snowden Distinguished Professor (DSP),the endowed chair previously held by Milton Friedman who received theNobel Memorial Prize in Economic Sciences.
Since 1974 Soare has established the now highy ranked mathemaaticallogic group at the University of Chicago. The new PhD’s brought to Chicagoby Soare described in §9 are among the best PhD’s in any branch of logic inthe last forty years. The current faculty in mathematical logic at Chicagoinclude Soare, Denis Hirschfeldt, and Maryanthe Malliaris, making Chicagoone of the top groups of mathematical logic in the country. The nearly twentyPhD students supervised by Soare and recently jointly advised by Soare andProfessor Denis Hirschfeldt listed in §10 are among the best in the last decadein computability and logic.
Soare has published five papers in the elite journals, of mathematics: TheAnnals of Mathematics, The Journal of the American Mathematical Society,
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and The Proceedings of the National Academy of Science. Soare’s Annalsof Mathematics paper on automorphisms was was chosen by Gerald Sacksas one of the most important papers in mathematical logic in the twentiethcentury as described in §6.
3 Educational Record
• A.B. Princeton University, 1963. Magna cum laude in Mathematics.
• Ph.D. in Mathematics, Cornell University, 1967.
4 Professional Record
Mar. 2012–Jul. 2012 Visiting Fellow, Isaac Newton Institute for Math-ematical Sciences, University of Cambridge, Cambridge U.K., Centen-nial year celebrating Alan Turing.
1994–present Paul Snowden Russell Distinguished Service Professor ofMathematics and Computer Science, University of Chicago.
1974–present Professor of Mathematics, University of Chicago.
Sept. 1989–Dec. 1989 Member, Mathematical Sciences Research Insti-tute, Berkeley, CA.
1988–1989 Visiting Professor, University of Heidelberg, Heidelberg, Ger-many.
1983–1987 Founding Chairman, Department of Computer Science, Uni-versity of Chicago.
1982–1983 Senior Research Fellow, partially supported by British Scienceand Engineering Research Council, staying mainly at University ofLeeds, with extended visits to Oxford University, University of Cam-bridge, University of Manchester, and University of Bristol.
1967–1973 Assistant Professor to Full Professor of Mathematics, Univer-sity of Illinois at Chicago.
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4.1 Editorial Duty:
1997–2009 A Managing Editor, Annals of Pure and Applied Logic.
1993–2002 Editor, Mathematical Logic Quarterly.
1982–2003 Editor, Information and Computation.
1983–1987 Advisory Editor, Annals of Pure and Applied Logic (Journalformerly called Annals of Mathematical Logic).
1971–1975 Associate Editor, Proceedings American Mathematical Society.
4.2 Honorary Societies:
Phi Beta KappaSociety of Sigma Xi
4.3 Professional Societies:
Association for Symbolic LogicAmerican Mathematical Society
5 Grants
NSF For over thirty-five years principal investigator of National ScienceFoundations grants in computability and mathematical logic.
2011–2016 Simons Foundation grant entitled, “Computability Theory andApplications.”
6 Honors and Recognition
June, 2011 Received the University of Chicago award for excellence in grad-uate teaching.
2003 Soare’s Annals of Mathematics paper [1974] was chosen by GeraldSacks (Harvard) as one of the thirty-one most important papers inmathematical logic in the twentieth century in his book:
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G. E. Sacks, Mathematical Logic in the 20th Century, Singapore Uni-versity Press, Singapore, and World Scientific Publishing Co. Series on20th Century Mathematics, Volume 6, Singapore, New Jersey, London,Hong Kong, 2003. ISBN: 981-02-4736-2 Printed in Singapore.
7 Invited Addresses at Leading Congresses
The most prestigious congress in this field is the International Congress ofMathematicians, and next the International Congress for Logic, Methodol-ogy and Philosophy of Science. The Association for Symbolic Logic is theprimary logic association in the U.S. and around the world. Its Centen-nial Meeting in June, 2000 was to celebrate the turn of the century, andthe plenary speakers were selected from leading scholars around the world.The organization Computability in Europe was has grown extremely fast andhas already attracted several hundred members in mathematics, computerscience, and related areas.
June 12–14, 2012 Speaker at Turing Centenary Workshop on The Incom-putable at the Kavli Royal Society International Centre, Chicheley Hall,UK.
www.mathcomp.leeds.ac.uk/turing2012/inc/
Apr. 2012 Opening plenary address, British Logic Colloquium, Universityof Kent at Canterbury, Conference on the work of Alan Turing.
Jun. 2007 Plenary speaker at Computability in Europe (CiE) Conferenceon Computation and Logic in the Real World, Siena, Italy, June 18–23,2007.
Jun. 2000 Plenary speaker at Centennial Meeting of the Association forSymbolic Logic, Urbana, Illinois.
Aug. 1995 International Congress for Logic, Methodology and Philosophyof Science, Florence, Italy.
Aug. 1991 International Congress for Logic, Methodology and PhilosophyUppsala, Sweden.
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Aug. 1979 International Congress for Logic, Methodology and Philosophyof Science, Hanover, Germany.
Aug. 1978 International Congress of Mathematicians, Helsinki, Finland.
8 Other Selected Invited Addresses
Mar.–Jul. 2012 The Isaac Newton Institute is hosting Soare for 3 monthsand has asked him to lecture at various British universities during hisvisit to the U.K.
Jan. 2012 MAMLS, Florida Atlantic University, Jan. 2–16, 2012, Logicand Computability, especially about Alan Turing.
Mar. 2011 North American Annual Meeting of Association for SymbolicLogic, Special Session on Definability Throughout Mathemaical Logic,in honor of Leo Harrington.
Jan. 2007 Topics in Computability, A meeting in honor of Richard Shore,Boston, Mass., Jan 21–22, 2007.
Aug. 2006 MATHLOGAPS Workshop, University of Leeds, Leeds, Eng-land, Aug. 21–25, 2006, five one hour lectures.
Jan. 2002 American Mathematical Society Special Session on Computabil-ity Theory, San Diego, CA. Robert Soare and his graduate student,Barbara Csima, were both invited speakers on their joint work fortwenty minutes each.
Jun. 1999 A.M.S. Workshop in Computability Theory and Applications,Boulder, Colorado. (One hour.)
Jul. 1997 European Summer Meeting of the Association for Symbolic Logic,Leeds, England. (One hour plenary speaker.)
Jul. 1997 Conference in Computability and Complexity, Kazan, Russia.(One hour lecture on mathematics plus TV interview conducted inRussian.)
Mar. 1996 University of Wisconsin, just prior to meeting of Associationfor Symbolic Logic. (One hour lecture on Kleene.)
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Jan. 1996 Conference on Computability Theory, Oberwolfach, Germany.(One hour lecture on computability plus one hour lecture on the workof S.C. Kleene.)
Jul. 1994 Conference on Computability Theory, University of Leeds, Leeds,U.K. (One hour lecture.)
Mar. 1994 Association for Symbolic Logic, Gainesville, FL. (One hour lec-ture.)
May, 1993 Sacks Symposium, A Symposium in Honor of Gerald Sacks onthe Occasion of his Sixtieth Birthday, MIT, Cambridge, Mass. (Onehour lecture.)
Jun. 1992 Logical Methods in Mathematics and Computer Science, A Sym-posium in Honor of Anil Nerode on the Occasion of his Sixtieth Birth-day, Cornell University, Ithaca, NY. (One hour lecture.)
Oct. 1989 Conference on Set Theory and the Continuum Hypothesis, atMath. Sci. Research Institute, in Berkeley, CA. (One hour lecture.)
Mar. 1989 Conference on Recursion Theory (organized by G. E. Sacks),Oberwolfach, W. Germany. (One hour lecture opening conference.)
Oct. 1987 Third Southeast Asian Conference on Mathematical Logic, Bei-jing, China. (One hour.)
Oct. 1984 Second Southeast Asian Logic Conference on Logic and its Rela-tion to Mathematics and Computer Science, Bangkok, Thailand. (Onehour lecture.)
Apr. 1984 Conference on Recursion Theory (organized by G. E. Sacks),Oberwolfach, W. Germany. (Forty-five minute lecture.)
Jul. 1983 Association for Symbolic Logic, Annual European Summer Meet-ing, Aachen, W. Germany. (Two one hour lectures.)
Apr. 1983 European Conference on Mathematical Logic, Oberwolfach, W.Germany. (One hour lecture.)
Jul. 1982 American Math. Soc. Summer Research Institute, Cornell Uni-versity. (Four one hour lectures.)
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Jul. 1981 Herbrand Memorial Logic Colloquium, Societe Francaise de Logique,Methodologie et Philosophie des Sciences. European ASL summermeeting, Marseilles, France. (One hour lecture.)
Aug. 1979 British logic colloquium ’79 on recursion theory, its generaliza-tions and applications, Leeds, England. (Four one hour lectures.)
9 New PhD’s Whom Soare Brought to Chicago
1. Sy Friedman; Ph.D. MIT, 1976; 1976-1978: Dickson Instructor, Uni-versity of Chicago; later Professor of Mathematics, MIT, and presentlyProfessor of Mathematics at the University of Vienna, Austria.
2. David Posner; Ph.D. 1976, Univ. of California at Berkeley; 1976-1978:Dickson Instructor, University of Chicago; later Assistant Professor ofMathematics, San Jose State University, and computer science consul-tant to computer industries in the area; currently working in computerindustry.
3. Phokion Kolaitis; Ph.D. 1978, UCLA; 1979-1981, Dickson Instructor,University of Chicago; Assistant Professor of Mathematics, OccidentalCollege, 1981–84, and 1985–86; Visiting Assistant Professor UCLA;1986–1987, worked at IBM Almaden; presently Professor of ComputerScience, Univ. of California at Santa Cruz.
4. Theodore Slaman; Ph.D. 1981, Harvard; 1981–1983: NSF PostdoctoralFellow University of Chicago; 1983–1996, Assistant Professor to Pro-fessor of Mathematics, University of Chicago; 1996–present, Professorand Chairman of Mathematics, Univ. of California at Berkeley, CA.
5. Stuart Kurtz; Ph.D. 1981, University of Illinois at Champaign-Urbana;1981–1983, Dickson Instructor University of Chicago; 1983–present,Assistant Professor to Professor and Chairman of Department of Com-puter Science, University of Chicago.
6. Christine Haught; Ph.D. 1985, Cornell University; 1987-1990, DicksonInstructor and NSF Postdoctoral Fellow, University of Chicago, cur-rently Professor of Mathematics at Loyola University, Chicago.
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7. Todd Hammond; Ph.D. 1990, Univ. of California at Berkeley; 1990–1994: Dickson Instructor and NSF Postdoctoral Fellow, University ofChicago; currently Professor of Mathematics at Truman State Univer-sity, Missouri.
8. David Seetapun; Ph.D. 1991, University of Cambridge, UK; 1991-1993: Dickson Instructor and NSF Postdoctoral Fellow, University ofChicago; currently in academics in computer science.
9. Andre Nies; Ph.D. 1992, University of Heidelberg; 1995–2002: Assis-tant Professor of Mathematics, University of Chicago; currently As-sociate Professor of Computer Science, University of Auckland, NewZealand, and Fellow of the Royal Society of New Zealand.
10. Denis Hirschfeldt; Ph.D. 1999, Cornell University; 2000–2008: DicksonInstructor to Full Professor of Mathematics, The University of Chicago;1999: Sacks Prize for the best Ph.D. thesis in logic on a world widebasis in any field.
11. Joseph Mileti; Ph.D. 2004, University of Illinois at Champaign Ur-bana; 2004–2007, Dickson Instructor and VIGRE postdoctoral fellow,University of Chicago; 2007–2010, Postdoc Dartmouth College.
12. Antonio Montalban, Ph.D. 2005, Cornell University; 2005–2011:, Dick-son Instructor to Associate Professor of Mathematics, The Universityof Chicago; 2005: Sacks Prize for the best Ph.D. thesis in logic on aworld wide basis in any field; 2009: AMS Centennial Fellowship; 2010:Packard Fellowship, $875,000.
13. Maryanthe Malllaris, Ph.D. 2009, University of California at Berke-ley, 2009–2013, Dickson Instructor in Mathematics, The University ofChicago; 2013–2016, Assistant Professorof Mathematics, The Univer-sity of Chicago.
10 Ph.D. Students Whom Soare Supervised:
1. Craig Smorynski, Ph.D. 1973, Mathematical Logic, University of Illi-nois at Chicago.
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2. Victor Bennison, Ph.D. 1976, Computer Science, University of Chicago;subsequently at Digital Equipment Corporation, and other computercompanies.
3. Michael Stob, Ph.D. 1979: 1979–1981: Moore Instructor in Mathemat-ics, M.I.T.; 1987: Visiting Assistant Professor of Mathematics, Univer-sity of Wisconsin, Madison, 1983-84; currently Professor of Mathemat-ics, and Dean of the College, Calvin College, Grand Rapids, MI.
4. Peter Fejer, Ph.D. 1980; 1980–1983, NSF Postdoctoral Fellow andH.C. Wang Assistant Professor of Mathematics, Cornell University;1983-present: Professor and Chairman, Department of Computer Sci-ence, U. Mass., Boston.
5. David Miller, Ph.D. 1981; 1981–present: Professor of Computer Sci-ence, Chairman and Dean, DePaul University.
6. Steven Schwarz, Ph.D. 1982; 1982–83: NSF Postdoctoral Fellow atM.I.T.; 1983–86: Assistant Professor in Computer Science Section ofDepartment of Mathematics, Tufts University; currently working in thecomputer industry.
7. Steffen Lempp, Ph.D. 1986; 1986–88: Gibbs Instructor of Mathematics,Yale University; 1988–present: Professor of Mathematics, University ofWisconsin, Madison, WI.
8. Kevin Wald, Ph.D. 1999; 1999–2002: Postdoctoral fellow, Univ. of Con-necticut, Storrs, CT, currently working in industry in Boston.
9. Russell Miller, Ph.D. 2000; 2000–2003: H.C. Wang Assistant Professorof Mathematics, Cornell University, 2004–present: Associate to FullProfessor of Mathematics, Queens College CUNY, New York.
10. Barbara Csima, Ph.D. 2003; 2003–2005 H.C. Wang Assistant Professorof Mathematics, Cornell University; 2005–present: Associate Professorof Mathematics, University of Waterloo, Waterloo, Canada.
11. Kenneth Harris, Ph.D. 2007; 2007–2010: Assistant Professor, Dept. ofMathematics, University of Michigan.
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12. Karen Lange, Ph.D. 2008; 2008–2011: NSF Postdoctoral Fellow andAssistant Professor at Notre Dame: 2011–present: Tenure track Assis-tant Professor of Mathematics, Wellesley College, MA.
13. Chris Conidis, Ph.D. 2009; 2009–2012: Postdoctoral Fellow at FieldsInstitute, Toronto, and Assistant Professor of Mathematics, Universityof Waterloo.
14. Rachel Epstein, Ph.D. 2010; 2010-2013: Benjamin Peirce AssistantProfessor of Mathematics, Harvard University.
15. Damir Dzhafarov, Ph.D. 2011; 2011–2012: NSF Postdoctoral Fellow,first year at Notre Dame, second and third year at University of Cali-fornia, Berkeley, 2013: Assistant Professor, University of Connecticut.
16. David Diamondstone, Ph.D. 2011: 2011-2012, Research Fellow, Uni-versity of Wellington, Wellington, New Zealand; 2013 researcher atMicrosoft.
17. Matthew Wright (2007–2013) Ph.D. 2013: Researcher at Drop BoxCorporation.
18. Jonathan Stephenson (2008–2014), Ph.D. expected 2014.
19. Eric Astor (2009–1015), Ph.D. expected 2015.
(The students after 2000 have been supervised by Soare jointly with Pro-fessor Denis Hirschfeldt.)
11 Books
Soare’s book [1987] has become the primary reference on computability the-ory for students and scholars doing research. It has been translated into Rus-sian and has been published in a Russian edition. It has also been printed inChina with the original English text for the mathematics and surroundingcomments in Chinese. This reflects the great popularity of the subject inRussia and China.
Soare is now working on a new computability book [CTA]. This will be-come the major book on the subject for mathematicians and computer sci-entists.
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1. Co-editor, Logic Year 1979–80, University of Connecticut, Lecture Notesin Mathematics No. 859, Springer-Verlag, 1981.
2. R. I. Soare, Recursively Enumerable Sets and Degrees: A Study of Com-putable Functions and Computably Generated Sets, Springer-Verlag,Heidelberg, 1987.
3. R. I. Soare, Mastering The Art of Turing Computability: Theory andApplications (CTA) , Springer-Verlag, to appear in 2014.
12 Publications in Elite Journals
The best journals for papers in mathematics are probably: The Annals ofMathematics, The Journal of the American Mathematical Society, and TheProceedings of the National Academy of Science. Soare has published fivepapers in these three elite journals over his career.
1. R. I. Soare, Automorphisms of the lattice of recursively enumerablesets I: maximal sets, Annals of Mathematics 100 (1974), 80–120.
2. L. Harrington and R. I. Soare, Post’s Program and incomplete re-cursively enumerable sets, Proc. Natl. Acad. of Sci. USA, 88 (1991),10242–10246.
3. T. Slaman and R.I. Soare, Algebraic aspects of the computably enu-merable degrees, Proc. Natl. Acad. of Sci. USA, 92 (1995) 617–621.
4. L. Harrington and R.I. Soare, The ∆03-automorphism method and non-
invariant classes of degrees, Journal of the Amer. Math. Soc., 9 (1996),617–666.
5. T. Slaman and R.I. Soare, Extension of embeddings in the computablyenumerable degrees, Annals of Mathematics, 154 (2001), 1–43.
13 Other Journal Articles
(1969a) Sets with no subsets of higher degree, J. Symbolic Logic, 34(1969), 53–56.
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(1969b) Recursion theory and Dedekind cuts. Trans. Amer. Math.Soc., 140 (1969), 271–294.
(1969c) A note on degrees of subsets, J. Symbolic Logic, 34 (1969),256.
(1969d) Constructive order types on cuts, J. Symbolic Logic, 34 (l969),285–289.
(1969e) Cohesive sets and recursively enumerable Dedekind cuts, Pa-cific J. Math., 31 (1969), 215–231.
(1970a) (with R. O. Gandy) A problem in the theory of constructiveorder types, J. Symbolic Logic, 35 (1970), 119–121.
(1970b) (with C. G. Jockusch, Jr.) Minimal covers and arithmeticalsets, Proc. Amer. Math. Soc., 25 (1970), 856–859.
(1971) (with C. G. Jockusch, Jr.) A minimal pair of Π01 classes, J.
Symbolic Logic, 26 (1971), 66–78.
(1972a) (with C. G. Jockusch, Jr.) Degrees of members of Π01 classes,
Pacific J. Math., 40 (1972), 605–616.
(1972b) (with C. G. Jockusch, Jr.) Π01 classes and degrees of theories
Trans. Amer. Math. Soc., 173 (1972), 33–35.
(1972c) The Friedberg-Muchnik theorem re-examined, Canadian J. ofMath., 24 (1972), 1070–1078.
(1973a) (with C. G. Jockusch, Jr.) Encodability of Kleene’s O, J.Symbolic Logic, 38 (1973), 437–440.
(1973b) (with C. G. Jockusch, Jr.) Post’s problem and his hypersimpleset, J. of Symbolic Logic, 38 (1973), 446–452.
(1974a) Automorphisms of the lattice of recursively enumerable sets,Bull. Amer. Math. Soc., 80 (1974), 53–58.
(1974b) Automorphisms of the lattice of recursively enumerable sets I:maximal sets, Ann. of Math. 100 (1974), 80–120.
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(1974c) Isomorphisms of countable vector spaces with recursive oper-ations, J. of the Australian Math. Society, 18 (1974), 230–235.
(1975) (with M. D. Morley) Boolean algebras, splitting theorems, and∆0
2 sets. Fund. Math., 90 (l975), 45–52.
(1976) The infinite injury priority method, J. Symbolic Logic, 41 (l976),513–530.
(1977) Computational complexity, speedable and levelable sets, J. Sym-bolic Logic, 42 (l977), 545–563.
(1978a) (with V. Bennison) Some lowness properties and computa-tional complexity sequences, Theoretical Computer Science, 6 (1978),233–254.
(1978c) (with M. Lerman and R. Shore) r-Maximal major subsets, Is-rael J. Math., 31 (1978), 1–18.
(1978d) Recursive enumerability, Proceedings of the International Congressof Mathematicians, Helsinki, 1978, 275–280.
(1980a) (with M. Lerman) d-Simple recursively enumerable sets, Pa-cific J. of Mathematics, 87 v (1980), 135–155.
(1980b) (with M. Lerman) A decidable fragment of the elementarytheory of the recursively enumerable sets, Trans. Amer. Math. Soc.,257 (1980), 1–37.
(1980c) Fundamental methods for constructing recursively enumerabledegrees, In: Recursion theory, its generalizations and applications,Logic Colloquium 79, Leeds, England, August 1979, London Mathe-matical Society Lecture Note Series 45, Cambridge University Press,1980.
(1980d) (with A. H. Lachlan) Not every finite lattice is embeddablein the recursively enumerable degrees, Advances in Mathematics, 37(1980), 74–82.
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(1981a) Constructions in the recursively enumerable degrees, In: Pro-ceedings of C.I.M.E. conference on “Recursion Theory and Computa-tional Complexity,” Bressanone, Italy, June 1979, published by liguoriEditore, Naples, Italy, 1981.
(1981b) (with P. Fejer) The plus cupping theorem in the recursivelyenumerable degrees, Proceedings of Logic Year 1979–80 at the Univer-sity of Connecticut, Lecture Notes in Mathematics No. 859, Springer-Verlag, 1981.
(1982a) Automorphisms of the lattice of recursively enumerable sets.II: Low sets, Annals of Mathematical Logic, 22 (l982), 69–107.
(1982b) Computational complexity of recursively enumerable sets. In-formation and Control 52 (1982), 8–18.
(1982c) (with M. Stob) Relative recursive enumerability, In: Pro-ceedings of the Herbrand Symposium Logic Colloquium ’81, Marseilles,France, editor, J. Stern, North-Holland, Amsterdam, (1982), 299–324.
(1984a) (with M. Lerman and R.A. Shore) The elementary theory ofthe recursively enumerable degrees is not ℵ0-categorical, Advances inMath, 53 (1984), 301–320.
(1984b) (with K. Ambos-Spies, C.G. Jockusch, Jr., and R. Shore) Analgebraic decomposition of the recursively enumerable degrees and thecoincidence of several degree classes with the promptly simple degrees,Trans. Amer. Math. Soc. 281 (1984), 109–128.
(1984c) (with J. Knight and A. H. Lachlan) Two theorems on degreesof models of true arithmetic, J. Symbolic Logic 49 (1984), 425–436.
(1985) Tree arguments in recursion theory and the 0′′′-priority method,In: Nerode and Shore (editors), Recursion Theory, Proc. Symp. PureMath. 42, Proceedings of the AMS-ASL Summer Institute on Recur-sion Theory, held at Cornell University June 28–July 16, 1982, Amer.Math. Soc., Providence, R. I., 1985, 53–106.
(1986) (with D. Cenzer, P. Clote, R. Smith, and S. Wainer) Membersof countable Π0
1 classes, Annals of Pure and Applied Logic 31 (1986),145–163.
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(1989a) (with C. G. Jockusch, Jr., M. Lerman, and R. M. Solovay)Recursively enumerable sets modulo iterated jumps and extensions ofArslanov’s completeness criterion, J. Symbolic Logic 54 (1989), 1288–1323.
(1989b) (with K. Ambos-Spies) The recursively enumerable degreeshave infinitely many one types, Annals of Pure and Applied Logic 44(1989), 1–23.
(1990) (with K. Ambos-Spies, and S. Homer) Minimal pairs and com-plete problems, Proceedings of Seventh Annual Symposium on Theo-retical Aspects of Computer Science, February, 1990, Rouen, France,C. Choffrut and T. Lengauer (editors), Lecture Notes in Computer Sci-ence, vol. 415, Springer-Verlag, Berlin, Heidelberg, New York, (1990)24–36.
(1991a) (with C. G. Jockusch, Jr.) Degrees of orderings not isomor-phic to recursive linear orderings, Annals of Pure and Applied Logic 52(1991), 39–64.
(1991b) (with L. Harrington) Post’s Program and incomplete recur-sively enumerable sets, Proc. Natl. Acad. of Sci. USA, 88 (1991),10242–10246.
(1991c) (with S. B. Cooper, L. Harrington, A. H. Lachlan, and S.Lempp) The d.r.e. degrees are not dense, Annals of Pure and AppliedLogic, 55 (1991), 125–151.
(1992) (with L. Harrington) Games in recursion theory and continu-ity properties of capping degrees, in: Set Theory and the Continuum,Proceedings of Workshop on Set Theory and the Continuum, Octo-ber, 1989, MSRI, Berkeley, CA, edited by H. Judah, W. Just, andW. H. Woodin, Springer-Verlag, 1992, 39–62.
(1993) (with K. Ambos-Spies, and A. H. Lachlan) The continuity ofcupping to 0′, Annals of Pure and Applied Logic, 64 (1993), 195–209.
(1994a) (with K. Ambos-Spies, and S. Homer) Minimal pairs and com-plete problems, Theoretical Computer Science, 132 (1994), 229–241.
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(1994b) (with A. H. Lachlan) Models of arithmetic and upper boundsfor arithmetic sets, J. of Symbolic Logic, 59 (1994), 977–983.
(1994c) (with C. G. Jockusch, Jr.) Boolean algebras, Stone spaces, andthe iterated Turing jump, J. of Symbolic Logic, 59 (1994), 1121–1138.
(1995) (with T. Slaman) Algebraic aspects of the computably enumer-able degrees, Proc. Natl. Acad. of Sci. USA, 92 (1995), 617–621.
(1995) (with L. Harrington) Dynamic properties of computably enu-merable sets, In: ‘Computability, Enumerability, Unsolvability: Direc-tions in Recursion Theory,’ eds. S. B. Cooper, T. A. Slaman, S. S. Wainer,Proceedings of the Recursion Theory Conference, University of Leeds,July, 1994, London Math. Soc. Lecture Notes Series, Cambridge Uni-versity Press, January 1996.
(1996a) (with L. Harrington) Definability, Automorphisms, and DynamicProperties of Computably Enumerable Sets, Bulletin of Symbolic Logic2 (1996), 199–213.
(1996b) Computability and recursion, Bulletin of Symbolic Logic 2(1996), 284–321.
(1996c) (with L. Harrington) The ∆03-automorphism method and non-
invariant classes of degrees, Journal of the Amer. Math. Soc., 9 (1996),617–666.
(1997) Computability and enumerability, Proceedings of the 10th In-ternational Congress for Logic, Methodology and the Philosophy ofScience, Section 3: Recursion Theory and Constructivism, Florence,August 19–25, 1995, In: Logic and Scientific Methods, ed. M.L. DallaChiara, K. Doets, D. Mundici, and J. van Benthem, Kluwer AcademicPublishers, The Netherlands, 1997, 221-237.
(1998a) (with L. Harrington) Definable properties of the computablyenumerable sets, Proceedings of the Oberwolfach Conference on Com-putability Theory, Annals of Pure and Applied Logic, 94 (1998), 97–125.
(1998b) (with L. Harrington) Codable Sets and Orbits of ComputablyEnumerable Sets, Journal of Symbolic Logic, 63 (1998), 1–28.
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(1998c) (with A. H. Lachlan) Models of arithmetic and subuniformbounds for arithmetic sets, Journal of Symbolic Logic, 63 (1998), 59–72.
(1999a) An overview of the computably enumerable sets, In: Handbookof Computability Theory, ed. E. Griffor, North-Holland, Amsterdam,1999, 199–248.
(1999b) The history and concept of computability, In: Handbook ofComputability Theory, ed. E. Griffor, North-Holland, Amsterdam, 1999,3–36.
(2000) Extensions, Automorphisms, and Definability, in: P. Cholak,S. Lempp, M. Lerman, and R. Shore, (eds.) Computability Theoryand its Applications: Current Trends and Open Problems, AmericanMathematical Society, Contemporary Math. #257, American Mathe-matical Society, Providence, RI, 2000. pps. 279–307.
(2001) T. Slaman and R. I. Soare, Extension of embeddings in thecomputably enumerable degrees, Annals of Math., 154 (2001), 1–43.
(2004a) R. I. Soare, Computability theory and differential geometry,Bull. Symb. Logic, Vol. 10 (2004), 457–486.
(2004b) B. F. Csima, D. R. Hirschfeldt, J. F. Knight, and R. I. Soare,Bounding prime models, J. Symbolic Logic, vol. 69 (2004), pp. 1117-1142.
(2006) B. F. Csima and R.I. Soare, Computability Results Used inDifferential Geometry, J. Symbolic Logic, vol. 71 (2006), pp. 1394–1410.
(2007a) B. F. Csima, V. Harizanov, D. R. Hirschfeldt, and R. I. Soare,Bounding Homogeneous Models, J. Symbolic Logic, vol. 72 (2007), pp.305–323.
(2007b) K. Lange and R.I. Soare, Computability of Homogeneous Mod-els, in: Proceedings of the Workshop on Vaught’s Conjecture, NotreDame University, May, 2005, Notre Dame Journal of Formal Logic,vol. 48, (2007), pp. 143–170.
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(2007c) R. I. Soare, Computability and Incomputability, Computationand Logic in the Real World, in: Proceedings of the Third Conferenceon Computability in Europe, CiE 2007, Siena, Italy, June 18–23, 2007,Lecture Notes in Computer Science, No. 4497, S.B. Cooper, B. Lowe,Andrea Sorbi (Eds.), Springer-Verlag, Berlin, Heidelberg, 2007.
(2009) R. I. Soare, Turing Oracle Machines, Online Computing, andThree Displacements in Computability Theory, Annals of Pure andApplied Logic, 160 (2009), 368–399.
(2010) D. Diamondstone, D. Dzhafarov and R. I. Soare, Π01-Classes,
Peano Arithmetic, Randomness, and Computable Domination, NotreDame Journal of Formal Logic, 50th Anniversary Issue, vol. 51 (2010),127–159.
(2012a) Arefin Huq, An interview with Robert Soare, A telephone in-terview by a graduate student, Arefin Huq with Robert Soare, Decem-ber 15, 2011, XRDS (Croosroads), the ACM magazine for students,Association of Computing Machinery, XRDS, Spring 2012, Vol. 18,No. 3, 2012.
(Technically, the graduate student, Arefin Huq, is the author, but hesimply transribed his interview with Robert Soare, and recorded Soare’sanswers exactly as given. It proved to be a very popular paper and waswidely circulated.)
(2012b) R. I. Soare, Formalism and intuition in computability theory.Philosophical Transactions of the Royal Society A, Phil Trans R Soc A2012;370 3277-3304.
(In this special issue of the Royal Society devoled to Turing, variousauthors were invited to contribute a paper of about twelve pages. How-ever, Soare was invited to contribute a paper of over forty pages, andhis was the lead article in this prestigious Royal Society journal.)
(2013a) R. I. Soare, Turing-Post Relativized Computability and Inter-active Computing, in: Jack Copeland, Carl Posy, and Oron Shagrir,
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(Editors), Computability: Godel, Church, Turing, and Beyond, MITPress, 2013, to appear.
(2013b) R. I. Soare, Turing and the Art of Classical Computability, in:Barry Cooper and Jan van Leeuwen (Editors), Alan Turing - His Workand Impact, Elsevier, 2013.
(2013c) R. I. Soare, Turing and the discovery of computability, in: Rod-ney Downey (Editor), Association for Symbolic Logic Lecture Notes inLogic, Cambridge University Press, 2013.
(2014) R. I. Soare, Why Turing’s Thesis is not a thesis, in: TuringCentenary Volume, Giovanni Sommaruga and Thomas Strahm (eds.)Birkhauser/Springer, Basel, 2014.
(2014) R. I. Soare, The Art of Turing Computability: Theory and Ap-plications, Computability in Europe Series, Springer-Verlag, Heidel-berg, 2014, to appear. (This book will be completed and sent to thepublisher by December, 2013 and will appear in 2014.)
![Turing-Post Relativized Computability and Interactive ...soare/Turing/shagrir.pdfTuring’s [1936] automatic machine (a-machine), now called simply a Turing machine, gave one such](https://static.documents.pub/doc/80x56/60ad846317ffd9574071b4bf/turing-post-relativized-computability-and-interactive-soareturingshagrirpdf.jpg)
