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Forcing with the Anti-Foundation axiom

โœ Scribed by Olivier Esser

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
121 KB
Volume
58
Category
Article
ISSN
0044-3050

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โœฆ Synopsis

Abstract

In this paper we define the forcing relation and prove its basic properties in the context of the theory ZFCA, i.e., ZFC minus the Foundation axiom and plus the Antiโ€Foundation axiom (AFA).

๐Ÿ“œ SIMILAR VOLUMES

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## Abstract We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Antiโ€Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing

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## Abstract The still unsettled decision problem for the restricted purely universal formulae ((โˆ€)~0~โ€formulae) of the first order setโ€theoretic language based over =, โˆˆ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related