Infinity and continuum in the alternative set theory.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00360959" target="_blank" >RIV/68407700:21240/22:00360959 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13194-021-00429-7" target="_blank" >https://doi.org/10.1007/s13194-021-00429-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13194-021-00429-7" target="_blank" >10.1007/s13194-021-00429-7</a>

Result language
angličtina
Original language name
Infinity and continuum in the alternative set theory.
Original language description
Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor’s set theory. Vopěnka criticised Cantor’s approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopˇenka grasps the phenomena of vagueness. Infinite sets are defined as sets containing proper semisets, i.e. vague parts of sets limited by the horizon. The new interpretation extends the field of applicability of mathematics and simultaneously indicates its limits. Compared to strict finitism and other attempts at a reduction of the infinite to the finite Vopˇenka’s theory reverses the process: he models the finite in the infinite.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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