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Abstract: In this paper we shall investigate fragments of Kripke--Platek set theory with Infinity which arise from the full theory by restricting Foundation to \Pi n Foundation, where n 2. The strength of such fragments will be characterized in terms of the smallest ordinal ff such that L ff is a model of every \Pi 2 sentence which is provable in the theory. 1 Introduction Kripke-Platek set theory plus Infinity (hereinafter called KP!) is a truly remarkable subsystem of ZF. Though considerably... (Update)
Context of citations to this paper: More
.... and sources for further reading are, for example, Jager [9, 10, 11, 13] Jager and Pohlers [15] Pohlers [18, 19, 20] and Rathjen [21, 22, 23, 24]. Arai [3, 4] presents an alternative proof theoretic approach to dealing with Mahlo universes. 8 5 Reductions to theories for...
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BibTeX entry: (Update)
M. Rathjen. Fragments of Kripke-Platek set theory with infinity. In P. Aczel, H. Simmons, and S. Wainer, editors, Proof Theory. Cambridge University Press, 1992. http://citeseer.ist.psu.edu/rathjen92fragments.html More
@misc{ rathjen92fragments,
author = "M. Rathjen",
title = "Fragments of Kripke-Platek set theory with infinity",
text = "M. Rathjen. Fragments of Kripke-Platek set theory with infinity. In P.
Aczel, H. Simmons, and S. Wainer, editors, Proof Theory. Cambridge University
Press, 1992.",
year = "1992",
url = "citeseer.ist.psu.edu/rathjen92fragments.html" }
Citations (may not include all citations):63 Admissible sets and structures (context) - BARWISE - 1975
40 Iterated inductive definitions and subsystems of analysis (context) - FEFERMAN, SIEG - 1981
19 Formal theories for transfinite iterations of generalized in.. (context) - FEFERMAN - 1970
18 Proof Theory (context) - UTTE - 1977
7 Functional interpretation of bar induction by bar recursion (context) - HOWARD - 1968
5 A simplified version of local predicativity (context) - BUCHHOLZ
4 Some applications of cut elimination (context) - SCHWICHTENBERG - 1977
4 Zur Beweistheorie der Kripke-Platek-Mengenlehre uber den nat.. (context) - AGER - 1983
3 A short course in ordinal analysis (context) - POHLERS
2 Ordinal analysis of bar recursion of type zero (context) - HOWARD - 1981
1 Non-extensional theories of predicative classes over PA (context) - CANTINI - 1982
1 A note on a theory of admissible sets with ffl--induction re.. (context) - CANTINI - 1983
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