Alternative set theory

From Open Encyclopedia

Generically, an alternative set theory is an alternative mathematical approach to the concept of set. It is a proposed alternative to the standard set theory.

Some of the alternative set theories are:

the theory of semisets;
rough set theory;
fuzzy set theory.
the set theory New Foundations
Positive set theory

Specifically, Alternative Set Theory (or AST) refers to a particular set theory developed in the 1970s and 1980s by Petr Vopěnka and his students. It builds on some ideas of the theory of semisets, but also introduces more radical changes: for example, 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.

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