Talk:List of alternative set theories

Infinite Sets in AST

... 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)

Relation AST in narrow sense and semisets

Should the article on semisets be expanded to discuss Alternative Set Theory in the more specific sense? Vkuncak (talk) 09:24, 17 January 2020 (UTC)

Are fuzzy sets rightly here?

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)

Split?

I'm thinking of splitting Alternative set theory into two articles: one article about Petr Vopěnka's Alternative Set Theory (currently a redirect to Alternative set theory), and another article talking about alternative set theories in general (basically a list of set theories that are not ZFC). We already have Category:Systems of set theory, and Set theory § Axiomatic set theory talks about ZFC and some alternatives, so the second article would be somewhat redundant. I guess one could just remove Alternative set theory § Other alternative set theories altogether and add a hatnote linking to Set theory § Axiomatic set theory instead. What do others think? – Tea2min (talk) 13:37, 19 February 2021 (UTC)

@Tea2min: I support creating a separate article about Vopěnka's alternative set theory, with an explicit description of its axioms and philosophical motivation (see e.g. , also available here).

Category:Systems of set theory currently includes some pages that are not theories, but concepts (fuzzy set, semiset, etc.) or references (On Numbers and Games). Not sure what to do about that.

I suggest renaming this article to "List of set theories" (like other "List of X" articles) and moving the content at Set_theory#Formalized_set_theory about various set theories and their categorization here, to avoid duplication of content and establish this as the canonical page. 2601:547:501:8F90:4952:5704:D79E:252C (talk) 17:38, 5 October 2022 (UTC)

References