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https://doi.org/10.1007/s00153-016-0501-z
| Title: | Fragments of Kripke–Platek set theory and the metamathematics of ? -recursion theory | Authors: | Friedman, S.-D Li, W Wong, T.L |
Issue Date: | 2016 | Publisher: | Springer New York LLC | Citation: | Friedman, S.-D, Li, W, Wong, T.L (2016). Fragments of Kripke–Platek set theory and the metamathematics of ? -recursion theory. Archive for Mathematical Logic 55 (43684) : 899-924. ScholarBank@NUS Repository. https://doi.org/10.1007/s00153-016-0501-z | Rights: | Attribution 4.0 International | Abstract: | The foundation scheme in set theory asserts that every nonempty class has an ? -minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and ?-recursion theory. We take KP set theory without foundation (called KP-) as the base theory. We show that KP- + ? 1-Foundation + V= L is enough to carry out finite injury arguments in ?-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. © 2016, The Author(s). | Source Title: | Archive for Mathematical Logic | URI: | https://scholarbank.nus.edu.sg/handle/10635/179282 | ISSN: | 0933-5846 | DOI: | 10.1007/s00153-016-0501-z | Rights: | Attribution 4.0 International |
| Appears in Collections: | Elements Staff Publications |
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