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arXiv · 2412.05914

Comparing Anti-foundation Axioms by Comparing Identity Conditions for Sets

Daheng Ju·Qihang Jing
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Abstract

In non-well-founded set theory, which anti-foundation axiom is philosophically justified, BAFA, FAFA, SAFA, AFA, or some other? In this paper, we investigate a general approach to answering this question: first, consider which identity condition for sets is justified; second, consider which anti-foundation axiom it justifies. Specifically, we study in detail two plausible identity conditions.

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Daheng Ju, Qihang Jing. 2024-12-08. Comparing Anti-foundation Axioms by Comparing Identity Conditions for Sets. https://arxiv.org/abs/2412.05914

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