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  • A NEW PERSPECTIVE ON SEMI-RETRACTIONS AND THE RAMSEY PROPERTY

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  • DANA BARTOŠOVÁ, LYNN SCOW
  • Journal:
    The Journal of Symbolic Logic / Volume 89 / Issue 3 / September 2024
    Published online by Cambridge University Press:
    08 March 2024, pp. 945-979
    Print publication:
    September 2024
    • Article
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  • 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 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.