A new perspective on semi-retractions and the Ramsey property

Dana Bartošová; Lynn Scow

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arXiv · 2204.10991

A new perspective on semi-retractions and the Ramsey property

Dana Bartošová·Lynn Scow

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Abstract

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.

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Dana Bartošová, Lynn Scow. 2022-04-23. A new perspective on semi-retractions and the Ramsey property. https://arxiv.org/abs/2204.10991

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