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arXiv · 2211.11020

Vop\v{e}nka's Alternative Set Theory in the Mathematical Canon of the 20th Century: Author's Translation from Czech

Zuzana Haniková
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Abstract

Vop\v{e}nka's Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem's construction of a nonstandard model of arithmetic, and its inception has been explicitly mentioned as an attempt to axiomatize Robinson's Nonstandard Analysis. Vop\v{e}nka preferred working in an axiomatic theory to investigating its individual models; he also viewed other areas of nonclassical mathematics through this prism. This article is a contribution to the mapping of the mathematical neighbourhood of the Alternative Set Theory, and at the same time, it submits a challenge to analyze in more detail the genesis and structure of the philosophical links that eventually influenced the Alternative Set Theory.

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Zuzana Haniková. 2022-11-20. Vop\v{e}nka's Alternative Set Theory in the Mathematical Canon of the 20th Century: Author's Translation from Czech. https://doi.org/10.46854/fc.2022.3r.485

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