Submission date: 23 April 2022

Abstract:

We investigate the notion of a semi-retraction between two first order structures (in typically different languages) 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.

Mathematics Subject Classification:

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Full text arXiv 2204.10991: pdf, ps.