Pac Structures as Invariants of Finite Group Actions

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Journal of Symbolic Logic:1-36 (forthcoming)
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Abstract

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.

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10.1017/jsl.2023.76

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Piotr Kowalski
Universität Regensburg

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References found in this work

Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
Model theoretic dynamics in Galois fashion.Daniel Max Hoffmann - 2019 - Annals of Pure and Applied Logic 170 (7):755-804.

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