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  • PAC STRUCTURES AS INVARIANTS OF FINITE GROUP ACTIONS

  • Part of
  • DANIEL MAX HOFFMANN, PIOTR KOWALSKI
  • Journal:
    The Journal of Symbolic Logic , First View
    Published online by Cambridge University Press:
    20 October 2023, pp. 1-36
    • Article
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  • We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered the PAC property is first order.