An argument for finsler-Aczel set theory

Mind 109 (434):241-253 (2000)
Recent interest in non-well-founded set theories has been concentrated on Aczel's anti-foundation axiom AFA. I compare this axiom with some others considered by Aczel, and argue that another axiom, FAFA, is superior in that it gives the richest possible universe of sets consistent with respecting the spirit of extensionality. I illustrate how using FAFA instead of AFA might result in an improvement to Barwise and Etchemendy's treatment of the liar paradox.
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DOI 10.1093/mind/109.434.241
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Luca Incurvati (2014). The Graph Conception of Set. Journal of Philosophical Logic 43 (1):181-208.
Albert Visser (2012). A Tractarian Universe. Journal of Philosophical Logic 41 (3):519-545.

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