On Wednesday 20 April 2005 23:57, Daniel Asimov wrote:
On of the Zermelo-Frankel axioms for set theory (the Axiom of Regularity, aka the Axiom of Foundation) implies the nonexistence of left-infinite epsilon chains. ... What do others think of possibly tossing out Regularity as a set theory axiom?
Well, e.g., Peter Aczel thought it was a good idea, so he wrote a book about it. And then Barwise and Moss thought so too, and wrote another. I expect there are several more :-). Aczel, "Non-well-founded sets", CSLI Lecture Notes #14. Barwise & Moss, "Vicious circles", CSLI Lecture Notes #60. If you ask Google about "antifoundation axioms", the first thing you find is a review of Barwise&Moss by Thomas Forster, who knows much about such things. -- g