Geometric condition for Dependent Choice
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911845448679424 |
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| author | Karagila, Asaf Schilhan, Jonathan |
| author_facet | Karagila, Asaf Schilhan, Jonathan |
| contents | We provide a geometric condition which characterises when the Principle of Dependent Choice holds in a Fraenkel--Mostowski--Specker permutation model. This condition is a slight weakening of requiring the filter of groups to be closed under countable intersections. We show that this condition holds nontrivially in a new permutation model we call "the nowhere dense model" and we study its extensions to uncountable cardinals as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_10261 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometric condition for Dependent Choice Karagila, Asaf Schilhan, Jonathan Logic Primary 03E25, Secondary 03E35 We provide a geometric condition which characterises when the Principle of Dependent Choice holds in a Fraenkel--Mostowski--Specker permutation model. This condition is a slight weakening of requiring the filter of groups to be closed under countable intersections. We show that this condition holds nontrivially in a new permutation model we call "the nowhere dense model" and we study its extensions to uncountable cardinals as well. |
| title | Geometric condition for Dependent Choice |
| topic | Logic Primary 03E25, Secondary 03E35 |
| url | https://arxiv.org/abs/2212.10261 |