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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.10991 |
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| _version_ | 1866913252268572672 |
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| author | Bartošová, Dana Scow, Lynn |
| author_facet | Bartošová, Dana Scow, Lynn |
| contents | We investigate the notion of a semi-retraction between two first order structures (in typically different signatures) that was introduced by the second author as a link between the Ramsey property and generalized indiscernible sequences. We further these connections between combinatorics and model theory, and look at semi-retractions through a new lens establishing transfers of the Ramsey property and finite Ramsey degrees under quite general conditions that are optimal as demonstrated by counterexamples. Finally, we compare semi-retractions to the category theoretic notion of a pre-adjunction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10991 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new perspective on semi-retractions and the Ramsey property Bartošová, Dana Scow, Lynn Logic Combinatorics We investigate the notion of a semi-retraction between two first order structures (in typically different signatures) that was introduced by the second author as a link between the Ramsey property and generalized indiscernible sequences. We further these connections between combinatorics and model theory, and look at semi-retractions through a new lens establishing transfers of the Ramsey property and finite Ramsey degrees under quite general conditions that are optimal as demonstrated by counterexamples. Finally, we compare semi-retractions to the category theoretic notion of a pre-adjunction. |
| title | A new perspective on semi-retractions and the Ramsey property |
| topic | Logic Combinatorics |
| url | https://arxiv.org/abs/2204.10991 |