Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-17T18:21:44.367Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE NON-ENUMERABILITY OF L

Published online by Cambridge University Press:  01 December 2016

G. E. SACKS
G. E. SACKS*
Affiliation:
MATHEMATICS DEPARTMENT HARVARD UNIVERSITY CAMBRIDGE, MA 02138, USA E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Assume V ≠ L. Then L is not E-Recursively Enumerable in any member of L via a forcing argument inspired by Friedberg [1]. This approach leads to an extension of Levy-Shoenfield absoluteness.

Keywords

E-recursionabsoluteness
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1396 - 1404
Copyright
Copyright © The Association for Symbolic Logic 2016 

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

Friedberg, R., A criterion for completeness of degrees of unsolvability, this JOURNAL, vol. 22 (1957), pp. 159–160.Google Scholar
[2] Friedman, S., Recursion on Inadmissible Ordinals , Ph.D. Thesis, MIT, 1976.Google Scholar
Kleene, S. C., Recursive functionals and quantifiers of finite type I . Transactions of the American Mathematical Society, vol. 91 (1959), pp. 1–52.Google Scholar
Lerman, M., Maximal α-r. e. sets . Transactions of the American Mathematical Society, vol. 181 (1974), pp. 341–386.Google Scholar
Moschovakis, Y., Descriptive Set Theory, North-Holland, Amsterdam, 1980.Google Scholar
Normann, D., Set recursion , Generalized Recursion Theory II, North-Holland, Amsterdam, 1978.Google Scholar
Sacks, G., Higher Recursion Theory, Springer-Verlag, Berlin, 1990.Google Scholar
Sacks, G., E-Recursive intuitions , Effective Mathematics of the Uncountable, Cambridge University Press, Cambridge, 2013.Google Scholar
Shore, R., Splitting an α-r. e. set . Transactions of the American Mathematical Society, vol. 204 (1975), pp. 65–77.Google Scholar
Simpson, S., Degree Theory on Admissible Ordinals, Proceedings of the 1972 Oslo Symposium, North-Holland, Amsterdam, 1974.Google Scholar