Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-17T12:13:46.819Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Proof of Friedman's Conjecture

Published online by Cambridge University Press:  15 January 2014

Liang Yu
Liang Yu*
Affiliation:
Institute of Mathematical Science and State key Laboratory for Novel Software Technology atNanjing University, Nanjing University, 210093, P.R. ofChinaE-mail: yuliang.nju@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a new proof of Friedman's conjecture that every uncountable set of reals has a member of each hyperdegree greater than or equal to the hyperjump.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 17 , Issue 3 , September 2011 , pp. 455 - 461
Copyright
Copyright © Association for Symbolic Logic 2011

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

REFERENCES

[1] Chong, C. T., Nies, André, and Yu, Liang, Lowness for higher randomness notions, Israel Journal of Mathematics, vol. 166 (2008), pp. 39–60.Google Scholar
[2] Friedman, Harvey, One hundred and two problems in mathematical logic, The Journal of Symbolic Logic, vol. 40 (1975), no. 2, pp. 113–129.Google Scholar
[3] Harrington, Leo, Analytic determinacy and 0# , The Journal of Symbolic Logic, vol. 43 (1978), no. 4, pp. 685–693.Google Scholar
[4] Hjorth, G., An argument due to Leo Harrington, unpublished.Google Scholar
[5] Hjorth, G. and Nies, A., Randomness in effective descriptive set theory, Journal of the London Mathematical Society, vol. 75 (2007), no. 2, pp. 495–508.Google Scholar
[6] Kechris, Alexander S., Martin, Donald A., and Robert M. Solovay, Introduction to Q-theory, Cabal seminar 79–81, Lecture Notes in Mathematics, vol. 1019, Springer, Berlin, 1983, pp. 199–282.Google Scholar
[7] Martin, Donald A., Proof of a conjecture of Friedman, Proceedings of the American Mathematical Society, vol. 55 (1976), no. 1, p. 129.Google Scholar
[8] Moschovaos, Yiannis N., Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland, Amsterdam, 1980.Google Scholar
[9] Nies, André, Computability and randomness, Oxford Logic Guides, vol. 51, Oxford University Press, Oxford, 2009.Google Scholar
[10] Sacks, Gerald E., Higher recursion theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1990.CrossRefGoogle Scholar
[11] Simpson, Stephen G., Minimal covers and hyperdegrees, Transactions of the American Mathematical Society, vol. 209 (1975), pp. 45–64.CrossRefGoogle Scholar