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"MoeBlee" <jazzmobe@xxxxxxxxxxx> writes:
> Yes, I understand that the absence of the axiom of regulairy is not the
> adoption of the negation of the axiom of regularity. So I mentioned the
> negation of the axiom of regularity indeed because it's a stronger
> condition (regarding the question we're dealing with) than just not
> having the axiom of regularity.
Most theories of anti-well-founded sets go further than just negating
the axiom of foundation (or regularity, if you prefer). They assert
something about what anti-well-founded sets exist. Aczel's axiom
says, essentially, that for every set of equations of appropriate
form, there exists a unique solution (and then we identify solutions
to distinct sets of equations up to bisimilarity).
See Barwise & Moss's /Vicious Circles/ for an introduction.
--
"Quincy, would you rather do epistemology or conceptual analysis?"
"You know what? I'd rather fight on an aircraft carrier.... And Mama
and Baba (Papa) would fight on an aircraft carrier, too."
-- Quincy P. Hughes, age 3 1/2
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