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GENERIC DERIVATIONS ON ALGEBRAICALLY BOUNDED STRUCTURES

Part of: Differential and difference algebra Model theory Connections with logic

Published online by Cambridge University Press:  13 November 2024

ANTONGIULIO FORNASIERO Open the ORCID record for ANTONGIULIO FORNASIERO [Opens in a new window]  and
GIUSEPPINA TERZO Open the ORCID record for GIUSEPPINA TERZO [Opens in a new window]
ANTONGIULIO FORNASIERO
Affiliation:
DIPARTIMENTO DI MATEMATICA E INFORMATICA “ULISSE DINI” UNIVERSITÀ DI FIRENZE E-mail: antongiulio.fornasiero@gmail.com URL: https://sites.google.com/site/antongiuliofornasiero/
GIUSEPPINA TERZO*
Affiliation:
DIPARTIMENTO DI MATEMATICA E APPLICAZIONI “RENATO CACCIOPPOLI” UNIVERSITÀ DEGLI STUDI DI NAPOLI “FEDERICO II”
*
E-mail: giuseppina.terzo@unina.it
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Abstract

Let ${\mathbb K}$ be an algebraically bounded structure, and let T be its theory. If T is model complete, then the theory of ${\mathbb K}$ endowed with a derivation, denoted by $T^{\delta }$, has a model completion. Additionally, we prove that if the theory T is stable/NIP then the model completion of $T^{\delta }$ is also stable/NIP. Similar results hold for the theory with several derivations, either commuting or non-commuting.

Keywords

derivationalgebraically boundedmodel completion

MSC classification

Primary: 03C60: Model-theoretic algebra 12H05: Differential algebra 12L12: Model theory
Secondary: 03C10: Quantifier elimination, model completeness and related topics

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Type
Article
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The Journal of Symbolic Logic , First View , pp. 1 - 27
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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