Kripke-Platek Set Theory and the Anti-Foundation Axiom

Mathematical Logic Quarterly 47 (4):435-440 (2001)
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Abstract

The paper investigates the strength of the Anti-Foundation Axiom, AFA, on the basis of Kripke-Platek set theory without Foundation. It is shown that the addition of AFA considerably increases the proof theoretic strength

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10.1002/1521-3870(200111)47:4

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Michael Rathjen
University of Leeds

Citations of this work

The strength of extensionality I—weak weak set theories with infinity.Kentaro Sato - 2009 - Annals of Pure and Applied Logic 157 (2-3):234-268.
The strength of extensionality II—weak weak set theories without infinity.Kentaro Sato - 2011 - Annals of Pure and Applied Logic 162 (8):579-646.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.
Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.
Subsystems of set theory and second order number theory.Wolfram Pohlers - 1998 - In Samuel R. Buss (ed.), Handbook of proof theory. New York: Elsevier. pp. 137--209.

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