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  1. Pac Structures as Invariants of Finite Group Actions.Daniel Max Hoffmann & Piotr Kowalski - forthcoming - Journal of Symbolic Logic:1-36.
    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 (...)
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  • Model theory of fields with free operators in characteristic zero.Rahim Moosa & Thomas Scanlon - 2014 - Journal of Mathematical Logic 14 (2):1450009.
    Generalizing and unifying the known theorems for difference and differential fields, it is shown that for every finite free algebra scheme.
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  • Geometric axioms for existentially closed Hasse fields.Piotr Kowalski - 2005 - Annals of Pure and Applied Logic 135 (1-3):286-302.
    We give geometric axioms for existentially closed Hasse fields. We prove a quantifier elimination result for existentially closed n-truncated Hasse fields and characterize them as reducts of existentially closed Hasse fields.
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  • Witt Vectors and Separably Closed Fields with Higher Derivations.Daniel Max Hoffmann - 2023 - Notre Dame Journal of Formal Logic 64 (2):173-184.
    The main scope of this short article is to provide a modification of the axioms given by Messmer and Wood for the theory of separably closed fields of positive characteristic and finite imperfectness degree. As their original axioms failed to meet natural expectations, a new axiomatization was given (i.e., Ziegler’s one), but the new axioms do not follow Messmer and Wood’s initial idea. Therefore, we aim to give a correct axiomatization that is more similar to the original one and that, (...)
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  • Existentially closed fields with finite group actions.Daniel M. Hoffmann & Piotr Kowalski - 2018 - Journal of Mathematical Logic 18 (1):1850003.
    We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a group scheme action.
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