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Fragments of Kripke-Platek set theory and the metamathematics of $$\alpha $$ -recursion theory.
- Source :
-
Archive for Mathematical Logic . Nov2016, Vol. 55 Issue 7/8, p899-924. 26p. - Publication Year :
- 2016
-
Abstract
- The foundation scheme in set theory asserts that every nonempty class has an $$\in $$ -minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and $$\alpha $$ -recursion theory. We take KP set theory without foundation (called KP $$^-$$ ) as the base theory. We show that KP $$^-$$ + $$\Pi _1$$ -Foundation + $$V=L$$ is enough to carry out finite injury arguments in $$\alpha $$ -recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09335846
- Volume :
- 55
- Issue :
- 7/8
- Database :
- Academic Search Index
- Journal :
- Archive for Mathematical Logic
- Publication Type :
- Academic Journal
- Accession number :
- 118670773
- Full Text :
- https://doi.org/10.1007/s00153-016-0501-z