{
  "id": "2204.10991",
  "version": "v1",
  "published": "2022-04-23T04:58:16.000Z",
  "updated": "2022-04-23T04:58:16.000Z",
  "title": "A new perspective on semi-retractions and the Ramsey property",
  "authors": [
    "Dana Bartošová",
    "Lynn Scow"
  ],
  "comment": "27 pages",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-23T04:58:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey property",
      "semi-retraction",
      "first order structures",
      "category theoretic notion",
      "finite ramsey degrees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}