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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | https://arxiv.org/abs/2305.10258 |
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| _version_ | 1866913430976331776 |
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| author | Nuida, Koji |
| author_facet | Nuida, Koji |
| contents | Zorn's Lemma is a well-known equivalent of the Axiom of Choice. It is usually regarded as a topic in axiomatic set theory, and its historically standard proof (from the Axiom of Choice) relies on transfinite recursion, a non-elementary set-theoretic machinery. However, the statement of Zorn's Lemma itself uses only elementary terminology for partially ordered sets. Therefore, it is worthy to establish a proof using only such elementary terminology. Following this line of study, we give a new simple proof of Zorn's Lemma, which does not even use the notion of a well-ordered set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10258 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Simple and Elementary Proof of Zorn's Lemma Nuida, Koji Logic Combinatorics 06A06, 03E25, 97E60 Zorn's Lemma is a well-known equivalent of the Axiom of Choice. It is usually regarded as a topic in axiomatic set theory, and its historically standard proof (from the Axiom of Choice) relies on transfinite recursion, a non-elementary set-theoretic machinery. However, the statement of Zorn's Lemma itself uses only elementary terminology for partially ordered sets. Therefore, it is worthy to establish a proof using only such elementary terminology. Following this line of study, we give a new simple proof of Zorn's Lemma, which does not even use the notion of a well-ordered set. |
| title | A Simple and Elementary Proof of Zorn's Lemma |
| topic | Logic Combinatorics 06A06, 03E25, 97E60 |
| url | https://arxiv.org/abs/2305.10258 |