Alternative set theory


In a general sense, an alternative set theory is any of the alternative mathematical approaches to the concept of set and an alternative to standard set theory.
Some of the alternative set theories are:
Specifically, Alternative Set Theory may refer 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 "formally" finite, which means that sets in AST satisfy the law of mathematical induction for set-formulas. However, some of these sets contain subclasses that are not sets, which makes them different from Cantor finite sets and they are called infinite in AST.