Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-06T10:36:48.402Z Has data issue: false hasContentIssue false

Π01 sets and models of WKL0

Published online by Cambridge University Press:  31 March 2017

Stephen G. Simpson
Affiliation:
Pennsylvania State University
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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Harvey, Friedman, Subsystems of second order arithmetic and their use in the formalization of mathematics, 19 pages, unpublished, March 1974.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.

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×