Aczel's set theory (AST) is consistent

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Feb 12, 2016 - Aczel's set theory [1] admits non-wellfounded sets, but has the wellfouned sets as a particular case. Aczel's set theory (AST) replaces the ...
Aczel’s set theory (AST) is consistent C´esar J. Rodrigues February 12, 2016 Research Gate (RG)

1 Consistency of Aczel’s set theory Aczel’s set theory [1] admits non-wellfounded sets, but has the wellfouned sets as a particular case. Aczel’s set theory (AST) replaces the foundation axiom of set theory by an anti-foundation axiom. From what we said above: con(ZF C) ⇒ con(AST ) Therefore, from the consistency of set theory [2] we conclude that AST is consistent.

References [1] P. Aczel. Non-Well-Founded Sets. CSLI Lecture Notes (14), Stanford, 1988. [2] C.J. Rodrigues. The consistency of set theory from the consistency of NFU set theory. Technical Report (R)esearch(G)ate, 2015.

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