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Π01 sets and models of WKL0

Published online by Cambridge University Press:  31 March 2017

Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] Oliver, Aberth, Computable Analysis, McGraw-Hill, 1980.
[2] J., Barwise (editor), Handbook of Mathematical Logic, Studies in Logic and the Foundations of Mathematics, North-Holland, 1977.
[3] Douglas, Cenzer and Jeffrey B., Remmel, Π0/1 classes in mathematics, [7], 1998, pp. 623–821.
[4] S. B., Cooper, T. A., Slaman, and S. S., Wainer (editors), Computability, Enumerability, Unsolvability: Directions in Recursion Theory, London Mathematical Society Lecture Notes, no. 224, Cambridge University Press, 1996.
[5] J. C. E., Dekker (editor), Recursive Function Theory, Proceedings of Symposia in Pure Mathematics, AmericanMathematical Society, 1962.
[6] F. R., Drake and J. K., Truss (editors), Logic Colloquium '86, Studies in Logic and the Foundations of Mathematics, North-Holland, 1988.
[7] Y. L., Ershov, S. S., Goncharov, A., Nerode, and J. B., Remmel (editors), Handbook of Recursive Mathematics, Studies in Logic and the Foundations of Mathematics, North-Holland, 1998.
[8] J.-E., Fenstad, I. T., Frolov, and R., Hilpinen (editors), Logic, Methodology and Philosophy of Science VIII, Studies in Logic and the Foundations of Mathematics, Elsevier, 1989.
[9] J.-E., Fenstad, I. T., Frolov, and R., Hilpinen (editors)FOM e-mail list, http://www.cs.nyu.edu/mailman/listinfo/fom/, September 1997 to the present.
[10] Harvey, Friedman, Subsystems of second order arithmetic and their use in the formalization of mathematics, 19 pages, unpublished, March 1974.
[11] Harvey, Friedman, Some systems of second order arithmetic and their use,Proceedings of the International Congress of Mathematicians, Vancouver 1974, vol. 1, Canadian Mathematical Congress, 1975, pp. 235–242.
[12] Kurt, Gödel, Collected Works, Oxford University Press, 1986–1995.
[13] L. A., Harrington, M., Morley, A., Scedrov, and S. G., Simpson (editors), Harvey Friedman 's Research on the Foundations of Mathematics, Studies in Logic and the Foundations of Mathematics, North-Holland, 1985.
[14] Thomas J., Jech, Set Theory, Pure and Applied Mathematics, Academic Press, New York, 1978.
[15] Carl G., Jockusch, Jr., Degrees of functions with no fixed points, [8], 1989, pp. 191–201.
[16] Carl G., Jockusch, Jr. and Robert I., Soare, Π0/1 classes and degrees of theories,Transactions of the American Mathematical Society, vol. 173 (1972), pp. 35–56.
[17] Richard, Kaye, Models of Peano Arithmetic, Oxford University Press, 1991.
[18] Antonín, Kučera, On the role of 0 in recursion theory, [6], 1988, pp. 133–141.
[19] Kenneth, Kunen, Set Theory, an Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, North-Holland, 1980.
[20] John, Myhill, Creative sets,Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 1 (1955), pp. 97–108.
[21] Michael E., Mytilinaios, Finite injury and Σ1 induction,The Journal of Symbolic Logic, vol. 54 (1989), pp. 38–49.
[22] Marian B., Pour-El and Saul, Kripke, Deduction-preserving “recursive isomorphisms” between theories,Fundamenta Mathematicae, vol. 61 (1967), pp. 141–163.
[23] Marian B., Pour-El and J., Ian Richards, Computability in Analysis and Physics, Perspectives inMathematical Logic, Springer-Verlag, 1988.
[24] Hartley, Rogers, Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.
[25] Dana S., Scott, Algebras of sets binumerable in complete extensions of arithmetic, [5], 1962, pp. 117–121.
[26] Dana S., Scott and Stanley, Tennenbaum, On the degrees of complete extensions of arithmetic (abstract), Notices of the American Mathematical Society, vol. 7 (1960), pp. 242–243.
[27] Stephen G., Simpson, Degrees of unsolvability: a survey of results, [2], 1977, pp. 631–652.
[28] Stephen G., Simpson, FOM: natural r.e. degrees; Pi01 classes, FOM e-mail list [9], August 13, 1999.Google Scholar
[29] Stephen G., Simpson, FOM: priority arguments; Kleene-r.e. degrees; Pi01 classes, FOM e-mail list [9], August 16, 1999.Google Scholar
[30] Stephen G., Simpson, Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, 1999.
[31] Stephen G., Simpson, Kazuyuki, Tanaka, and Takeshi, Yamazaki, Some conservation results on weak König's lemma,Annals of Pure and Applied Logic, vol. 118 (2002), pp. 87–114.
[32] Raymond M., Smullyan, Theory of Formal Systems, Annals of Mathematics Studies, Princeton University Press, 1961.
[33] Robert I., Soare, Recursively Enumerable Sets and Degrees, Perspectives inMathematical Logic, Springer-Verlag, 1987.
[34] Andrea, Sorbi, The Medvedev lattice of degrees of difficulty, [4], 1996, pp. 289–312.
[35] Kazuyuki, Tanaka, More on models of WKL0 (see also [36]), 4 pages, handwritten, 1995.
[36] Kazuyuki, Tanaka, (in Japanese), Sūrikaisekikenkyūsho Kōkyūroku, vol. 976 (1997), pp. 77–85.
[37] J., van Heijenoort (editor), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, 1967.

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