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MODEL THEORY OF DERIVATIONS OF THE FROBENIUS MAP REVISITED

Part of: Model theory Differential and difference algebra

Published online by Cambridge University Press:  10 November 2021

JAKUB GOGOLOK Open the ORCID record for JAKUB GOGOLOK [Opens in a new window]
JAKUB GOGOLOK*
Affiliation:
INSTYTUT MATEMATYCZNY UNIWERSYTET WROCŁAWSKI WROCŁAW, POLAND URL: http://www.math.uni.wroc.pl/~gogolok/
*
E-mail: jakub.gogolok@math.uni.wroc.pl
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Abstract

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 a quantifier elimination result, which holds in a much more general context and we suggest a way of giving “one-dimensional” axiomatizations for model companions of some theories of fields with operators.

Keywords

derivations of the Frobenius mapquantifier elimination

MSC classification

Primary: 03C10: Quantifier elimination, model completeness and related topics 03C60: Model-theoretic algebra
Secondary: 12H05: Differential algebra
Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 3 , September 2023 , pp. 1213 - 1229
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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