Talk:Alternative set theory

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 Field: Foundations, logic, and set theory

Infinite Sets in AST[edit]

... all sets are finite (though some are "nonstandard finite" 
and externally actually infinite, and there are also classes
which can be infinite even internally) in AST. ...

What do you mean by "externally" and "internally" infinite? There is an infinite set defined in AST as a set containing a proper class as its subclass. --Gogino 05:32, 2 November 2006 (UTC)

Are fuzzy sets rightly here?[edit]

Are fuzzy sets etc rightly part of alternative set theory? Is there any citations that talk about them as such as they cannot be used as a basis for deriving big chunks of mathematics from - they are more for heuristic use in real world knowledge based applications dealing with uncertainty. Dmcq (talk) 07:19, 23 July 2009 (UTC)

Well, there's a version of ZFC in Gödel–Dummett logic (whose classification as a fuzzy logic is questionable) by Takeuti and Titani, and there are some recent proposals like Fuzzy Class Theory by Běhounek and Cintula[1][2][3]. So far they basically did not get anywhere past the stage of defining the axiom system. I'd say that for all practical purposes you are correct. — Emil J. 10:44, 23 July 2009 (UTC)