Alternative set theory  From Wikipedia, the free encyclopedia
Jump to: navigation, search  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:  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
"formally" finite, which means that sets in AST satisfy the law
of mathematical induction for set-formulas (more precisely: the
part of AST that consists of axioms related to sets only is
equivalent to the Zermelo–Fraenkel (or ZF) set theory, in which
the axiom of infinity is replaced by its negation). However,
some of these sets contain subclasses that are not sets, which
makes them different from Cantor (ZF) finite sets and they are
called infinite in AST.