Alternative set theory has been created and, together with his colleagues at Charles Univ., developed by P. Vopěnka since the 1970s. In agreement with Husserl’s phenomenology, he based his theory on the natural world and the human view thereof.
The most important for any set theory is the way it treats infinity. A different approach to infinity forms the key difference between AST and classical set theories based on the Cantor set theory (CST). Cantor’s approach led to the creation of a rigid, abstract world with an enormous scale of infinite cardinalities while Vopěnka’s infinity, based on the notion of horizon, is more natural and acceptable.
Another source of inspiration were nonstandard models of Peano arithmetics with infinitely large (nonstandard) numbers. The way to build them in AST is easy and natural.
Classes, Sets and Semisets
AST, as well as CST, builds on notions of’ set’, ‘class’, ‘element of a set’ and, in addition, introduces...
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Vopěnka, P., Trlifajová, K. (2001). Alternative Set Theory . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_9
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