Very basic set theory
History and Overview
2026-01-29 v8 Logic
Abstract
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.
Cite
@article{arxiv.2303.13473,
title = {Very basic set theory},
author = {Doeko Homan},
journal= {arXiv preprint arXiv:2303.13473},
year = {2026}
}
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8 pages