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We define the interpolative fusion T∪∗ of a family i∈I of first-order theories over a common reduct T∩, a notion that generalizes many examples of random or generic structures in the model-theo... |
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Let G be a finite group. We explore the model-theoretic properties of the class of differential fields of characteristic zero in m commuting derivations equipped with a G-action by differential fie... |
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We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree. |
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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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We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by Wood in the case of the theory $\operatorname {DCF}_p$ and that it eliminates quantifiers after adding the inverse of the Frobenius map to the language. This strengthens the results from [4]. As a by-product, we get a new geometric axiomatization of this model companion. Along the way we also prove (...) |
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We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé (...) |
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Nous isolons des propriétés valables dans certaines théories de purs corps ou de corps munis d’opérateurs afin de montrer qu’une théorie est simple lorsque les clôtures définissables et algébriques sont contrôlées par une théorie stable associée. |
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