Very basic set theory
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917227717984256 |
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| author | Homan, Doeko |
| author_facet | Homan, Doeko |
| contents | Ernst Zermelo's axiomatization of set theory (1908) did not exclude `a set that is a member of itself'. We call a set that is a member of itself `an individual'. In this article we prove the elimination of Russell's paradox is equivalent to "For every set S, an individual is a member of S or a set (but not an individual) is not a member of S". This shows there is place in set theory for individuals. And we show the set theory with individuals has its philosophical foundation in Ludwig Wittgenstein's Tractatus Logico-Philosophicus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13473 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Very basic set theory Homan, Doeko History and Overview Logic math.lo Ernst Zermelo's axiomatization of set theory (1908) did not exclude `a set that is a member of itself'. We call a set that is a member of itself `an individual'. In this article we prove the elimination of Russell's paradox is equivalent to "For every set S, an individual is a member of S or a set (but not an individual) is not a member of S". This shows there is place in set theory for individuals. And we show the set theory with individuals has its philosophical foundation in Ludwig Wittgenstein's Tractatus Logico-Philosophicus. |
| title | Very basic set theory |
| topic | History and Overview Logic math.lo |
| url | https://arxiv.org/abs/2303.13473 |