The Anti-foundation Axiom in Constructive Set Theories
نویسنده
چکیده
The paper investigates the strength of the anti-foundation axiom on the basis of various systems of constructive set theories. 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in diiering elds such as mathematical logic, computer science , artiicial intelligence, linguistics, cognitive science, and philosophy. Logicians rst explored set theories whose universe contains what are called non-wellfounded sets, or hypersets (cf. 17], 5]). But the area was considered rather exotic until these theories were put to use in developing rigorous accounts of circular notions in computer science (cf. 7]). Instead of the Foundation Axiom these set theories adopt
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Kripke-Platek Set Theory and the Anti-Foundation Axiom
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