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 13 Other Journal Articles 13

2 1 Address

Department of Mathematics University of Chicago 5734 University Avenue Chicago, IL 60637 (773) 702-6029 e-mail: [email protected]

2 Short Biography

Robert Irving Soare was born in Orange, New Jersey, and graduated from Newark Academy in 1959. At Princeton from 1959 to 1963, he studied mathematical logic and computability theory with Alonzo Church and wrote a senior thesis with Church and his associate. He studied logic and computability at Cornell from 1963 to 1967 and wrote a Ph.D. thesis wth Anil Nerode in 1967. From 1967 to 1973 he rose from Assistant Professor to full professor of mathematics at the University of Illinois at Chicago (UIC). In 1974 he moved 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 of Computer Sciece by the University President Hanna Gray. In 1994 Presicent Sonnenschein named Soare the Paul Snowden Distinguished Professor (DSP), the endowed chair previously held by Milton Friedman who received the Nobel Memorial Prize in Economic Sciences. Since 1974 Soare has established the now highy ranked mathemaatical logic group at the University of Chicago. The new PhD’s brought to Chicago by Soare described in §9 are among the best PhD’s in any branch of logic in the last forty years. The current faculty in mathematical logic at Chicago include Soare, Denis Hirschfeldt, and Maryanthe Malliaris, making Chicago one of the top groups of mathematical logic in the country. The nearly twenty PhD students supervised by Soare and recently jointly advised by Soare and Professor Denis Hirschfeldt listed in §10 are among the best in the last decade in computability and logic. Soare has published ﬁve papers in the elite journals, of mathematics: The Annals of Mathematics, The Journal of the American Mathematical Society,

3 and The Proceedings of the National Academy of Science. Soare’s Annals of Mathematics paper on automorphisms was was chosen by Gerald Sacks as one of the most important papers in mathematical logic in the twentieth century 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 of Mathematics 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 Science and Engineering Research Council, staying mainly at University of Leeds, 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.

4 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 (Journal formerly called Annals of Mathematical Logic).

1971–1975 Associate Editor, Proceedings American Mathematical Society.

4.2 Honorary Societies: Phi Beta Kappa Society of Sigma Xi

4.3 Professional Societies: Association for Symbolic Logic American Mathematical Society

5 Grants

NSF For over thirty-ﬁve years principal investigator of National Science Foundations grants in computability and mathematical logic.

2011–2016 Simons Foundation grant entitled, “Computability Theory and Applications.”

6 Honors and Recognition

June, 2011 Received the University of Chicago award for excellence in graduate teaching.

2003 Soare’s Annals of Mathematics paper [1974] was chosen by Gerald Sacks (Harvard) as one of the thirty-one most important papers in mathematical logic in the twentieth century in his book:

5 G. E. Sacks, Mathematical Logic in the 20th Century, Singapore Uni- versity Press, Singapore, and World Scientiﬁc Publishing Co. Series on 20th 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 of Mathematicians, and next the International Congress for Logic, Methodol- ogy and Philosophy of Science. The Association for Symbolic Logic is the primary 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, and the plenary speakers were selected from leading scholars around the world. The organization Computability in Europe was has grown extremely fast and has already attracted several hundred members in mathematics, computer science, 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, University of Kent at Canterbury, Conference on the work of Alan Turing.

Jun. 2007 Plenary speaker at Computability in Europe (CiE) Conference on Computation and Logic in the Real World, Siena, Italy, June 18–23, 2007.

Jun. 2000 Plenary speaker at Centennial Meeting of the Association for Symbolic Logic, Urbana, Illinois.

Aug. 1995 International Congress for Logic, Methodology and Philosophy of Science, Florence, Italy.

Aug. 1991 International Congress for Logic, Methodology and Philosophy Uppsala, Sweden.

6 Aug. 1979 International Congress for Logic, Methodology and Philosophy of 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 months and has asked him to lecture at various British universities during his visit to the U.K. Jan. 2012 MAMLS, Florida Atlantic University, Jan. 2–16, 2012, Logic and Computability, especially about Alan Turing. Mar. 2011 North American Annual Meeting of Association for Symbolic Logic, 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 for twenty 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 in Russian.) Mar. 1996 University of Wisconsin, just prior to meeting of Association for Symbolic Logic. (One hour lecture on Kleene.)

7 Jan. 1996 Conference on Computability Theory, Oberwolfach, Germany. (One hour lecture on computability plus one hour lecture on the work of 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 lecture.)

May, 1993 Sacks Symposium, A Symposium in Honor of Gerald Sacks on the Occasion of his Sixtieth Birthday, MIT, Cambridge, Mass. (One hour 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, at Math. 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. (One hour 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.)

8 Jul. 1981 Herbrand Memorial Logic Colloquium, Soci´et´eFrancaise de Logique, Methodologie et Philosophie des Sciences. European ASL summer meeting, Marseilles, France. (One hour lecture.)

Aug. 1979 British logic colloquium ’79 on recursion theory, its generalizations 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 presently Professor 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 of Mathematics, San Jose State University, and computer science consul- tant to computer industries in the area; currently working in computer industry.

3. Phokion Kolaitis; Ph.D. 1978, UCLA; 1979-1981, Dickson Instructor, University of Chicago; Assistant Professor of Mathematics, Occidental College, 1981–84, and 1985–86; Visiting Assistant Professor UCLA; 1986–1987, worked at IBM Almaden; presently Professor of Computer Science, Univ. of California at Santa Cruz.

4. Theodore Slaman; Ph.D. 1981, Harvard; 1981–1983: NSF Postdoctoral Fellow University of Chicago; 1983–1996, Assistant Professor to Pro- fessor of Mathematics, University of Chicago; 1996–present, Professor and 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, Dickson Instructor and NSF Postdoctoral Fellow, University of Chicago, currently Professor of Mathematics at Loyola University, Chicago.

9 7. Todd Hammond; Ph.D. 1990, Univ. of California at Berkeley; 1990– 1994: Dickson Instructor and NSF Postdoctoral Fellow, University of Chicago; 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 of Chicago; 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, New Zealand, and Fellow of the Royal Society of New Zealand.

10. Denis Hirschfeldt; Ph.D. 1999, Cornell University; 2000–2008: Dickson Instructor to Full Professor of Mathematics, The University of Chicago; 1999: Sacks Prize for the best Ph.D. thesis in logic on a world wide basis 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 University of Chicago; 2005: Sacks Prize for the best Ph.D. thesis in logic on a world 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 of Chicago; 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.

10 2. Victor Bennison, Ph.D. 1976, Computer Science, University of Chicago; subsequently at Digital Equipment Corporation, and other computer companies.

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 and H.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 at M.I.T.; 1983–86: Assistant Professor in Computer Science Section of Department of Mathematics, Tufts University; currently working in the computer industry.

7. Steﬀen Lempp, Ph.D. 1986; 1986–88: Gibbs Instructor of Mathematics, Yale University; 1988–present: Professor of Mathematics, University of Wisconsin, 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 Professor of Mathematics, Cornell University, 2004–present: Associate to Full Professor of Mathematics, Queens College CUNY, New York.

10. Barbara Csima, Ph.D. 2003; 2003–2005 H.C. Wang Assistant Professor of Mathematics, Cornell University; 2005–present: Associate Professor of Mathematics, University of Waterloo, Waterloo, Canada.

11. Kenneth Harris, Ph.D. 2007; 2007–2010: Assistant Professor, Dept. of Mathematics, University of Michigan.

11 12. Karen Lange, Ph.D. 2008; 2008–2011: NSF Postdoctoral Fellow and Assistant 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 Fields Institute, Toronto, and Assistant Professor of Mathematics, University of Waterloo.

14. Rachel Epstein, Ph.D. 2010; 2010-2013: Benjamin Peirce Assistant Professor 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 at Microsoft.

17. Matthew Wright (2007–2013) Ph.D. 2013: Researcher at Drop Box Corporation.

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 theory 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 in China with the original English text for the mathematics and surrounding comments in Chinese. This reﬂects the great popularity of the subject in Russia and China. Soare is now working on a new computability book [CTA]. This will become the major book on the subject for mathematicians and computer sci- entists.

12 1. Co-editor, Logic Year 1979–80, University of Connecticut, Lecture Notes in 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 and Applications (CTA) , Springer-Verlag, to appear in 2014.

12 Publications in Elite Journals

The best journals for papers in mathematics are probably: The Annals of Mathematics, The Journal of the American Mathematical Society, and The Proceedings of the National Academy of Science. Soare has published ﬁve papers in these three elite journals over his career.

1. R. I. Soare, Automorphisms of the lattice of recursively enumerable sets I: maximal sets, Annals of Mathematics 100 (1974), 80–120.

2. L. Harrington and R. I. Soare, Post’s Program and incomplete recursively enumerable sets, Proc. Natl. Acad. of Sci. USA, 88 (1991), 10242–10246.

3. T. Slaman and R.I. Soare, Algebraic aspects of the computably enumerable degrees, Proc. Natl. Acad. of Sci. USA, 92 (1995) 617–621.

0 4. L. Harrington and R.I. Soare, The ∆3-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 computably enumerable 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.

13 (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 constructive order types, J. Symbolic Logic, 35 (1970), 119–121.

(1970b) (with C. G. Jockusch, Jr.) Minimal covers and arithmetical sets, Proc. Amer. Math. Soc., 25 (1970), 856–859.

0 (1971) (with C. G. Jockusch, Jr.) A minimal pair of Π1 classes, J. Symbolic Logic, 26 (1971), 66–78.

0 (1972a) (with C. G. Jockusch, Jr.) Degrees of members of Π1 classes, Paciﬁc J. Math., 40 (1972), 605–616.

0 (1972b) (with C. G. Jockusch, Jr.) Π1 classes and degrees of theories Trans. Amer. Math. Soc., 173 (1972), 33–35.

(1972c) The Friedberg-Muchnik theorem re-examined, Canadian J. of Math., 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 hypersimple set, 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.

14 (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 computational complexity sequences, Theoretical Computer Science, 6 (1978), 233–254.

(1978b) Recursively enumerable sets and degrees, Bull. Amer. Math. Soc, 84 (l978), 1149–1181.

(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 Congress of 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 elementary theory of the recursively enumerable sets, Trans. Amer. Math. Soc., 257 (1980), 1–37.

(1980c) Fundamental methods for constructing recursively enumerable degrees, 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 embeddable in the recursively enumerable degrees, Advances in Mathematics, 37 (1980), 74–82.

15 (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 liguori Editore, Naples, Italy, 1981.

(1981b) (with P. Fejer) The plus cupping theorem in the recursively enumerable 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 of the recursively enumerable degrees is not ℵ0-categorical, Advances in Math, 53 (1984), 301–320.

(1984b) (with K. Ambos-Spies, C.G. Jockusch, Jr., and R. Shore) An algebraic decomposition of the recursively enumerable degrees and the coincidence 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 degrees of models of true arithmetic, J. Symbolic Logic 49 (1984), 425–436.

(1985) Tree arguments in recursion theory and the 0000-priority method, In: Nerode and Shore (editors), Recursion Theory, Proc. Symp. Pure Math. 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) Members 0 of countable Π1 classes, Annals of Pure and Applied Logic 31 (1986), 145–163.

16 (1989a) (with C. G. Jockusch, Jr., M. Lerman, and R. M. Solovay) Recursively enumerable sets modulo iterated jumps and extensions of Arslanov’s completeness criterion, J. Symbolic Logic 54 (1989), 1288– 1323.

(1989b) (with K. Ambos-Spies) The recursively enumerable degrees have 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 recursively 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 Applied Logic, 55 (1991), 125–151.

(1992) (with L. Harrington) Games in recursion theory and continuity 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, and W. H. Woodin, Springer-Verlag, 1992, 39–62.

(1993) (with K. Ambos-Spies, and A. H. Lachlan) The continuity of cupping to 00, 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.

17 (1994b) (with A. H. Lachlan) Models of arithmetic and upper bounds for arithmetic sets, J. of Symbolic Logic, 59 (1994), 977–983.

(1994c) (with C. G. Jockusch, Jr.) Boolean algebras, Stone spaces, and the iterated Turing jump, J. of Symbolic Logic, 59 (1994), 1121–1138.

(1995) (with T. Slaman) Algebraic aspects of the computably enumerable degrees, Proc. Natl. Acad. of Sci. USA, 92 (1995), 617–621.

(1995) (with L. Harrington) Dynamic properties of computably enumerable 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 Dynamic Properties of Computably Enumerable Sets, Bulletin of Symbolic Logic 2 (1996), 199–213.

(1996b) Computability and recursion, Bulletin of Symbolic Logic 2 (1996), 284–321.

0 (1996c) (with L. Harrington) The ∆3-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 of Science, Section 3: Recursion Theory and Constructivism, Florence, August 19–25, 1995, In: Logic and Scientiﬁc Methods, ed. M.L. Dalla Chiara, K. Doets, D. Mundici, and J. van Benthem, Kluwer Academic Publishers, The Netherlands, 1997, 221-237.

(1998a) (with L. Harrington) Deﬁnable properties of the computably enumerable 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 Computably Enumerable Sets, Journal of Symbolic Logic, 63 (1998), 1–28.

18 (1998c) (with A. H. Lachlan) Models of arithmetic and subuniform bounds for arithmetic sets, Journal of Symbolic Logic, 63 (1998), 59– 72.

(1999a) An overview of the computably enumerable sets, In: Handbook of Computability Theory, ed. E. Griﬀor, North-Holland, Amsterdam, 1999, 199–248.

(1999b) The history and concept of computability, In: Handbook of Computability 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 Theory and its Applications: Current Trends and Open Problems, American Mathematical 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 the computably 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 in Diﬀerential 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, Notre Dame University, May, 2005, Notre Dame Journal of Formal Logic, vol. 48, (2007), pp. 143–170.

19 (2007c) R. I. Soare, Computability and Incomputability, Computation and Logic in the Real World, in: Proceedings of the Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18–23, 2007, Lecture Notes in Computer Science, No. 4497, S.B. Cooper, B. L¨owe, Andrea Sorbi (Eds.), Springer-Verlag, Berlin, Heidelberg, 2007.

(2009) R. I. Soare, Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory, Annals of Pure and Applied Logic, 160 (2009), 368–399.

0 (2010) D. Diamondstone, D. Dzhafarov and R. I. Soare, Π1-Classes, Peano Arithmetic, Randomness, and Computable Domination, Notre Dame Journal of Formal Logic, 50th Anniversary Issue, vol. 51 (2010), 127–159.

(2012a) Areﬁn Huq, An interview with Robert Soare, A telephone interview 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 he simply transribed his interview with Robert Soare, and recorded Soare’s answers exactly as given. It proved to be a very popular paper and was widely circulated.)

(2012b) R. I. Soare, Formalism and intuition in computability theory. Philosophical Transactions of the Royal Society A, Phil Trans R Soc A 2012;370 3277-3304.

(In this special issue of the Royal Society devoled to Turing, various authors were invited to contribute a paper of about twelve pages. How- ever, Soare was invited to contribute a paper of over forty pages, and his was the lead article in this prestigious Royal Society journal.)

http://rsta.royalsocietypublishing.org/cgi/content/abstract/370/1971/3277

(2013a) R. I. Soare, Turing-Post Relativized Computability and Inter- active Computing, in: Jack Copeland, Carl Posy, and Oron Shagrir,

20 (Editors), Computability: G¨odel,Church, Turing, and Beyond, MIT Press, 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 Work and Impact, Elsevier, 2013.

(2013c) R. I. Soare, Turing and the discovery of computability, in: Rod- ney Downey (Editor), Association for Symbolic Logic Lecture Notes in Logic, Cambridge University Press, 2013.

(2014) R. I. Soare, Why Turing’s Thesis is not a thesis, in: Turing Centenary Volume, Giovanni Sommaruga and Thomas Strahm (eds.) Birkh¨auser/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 the publisher by December, 2013 and will appear in 2014.)