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arXiv · 2412.14862

Canonical quotients in model theory

Adrián Portillo Fernández
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Abstract

We study canonical quotients in model theory, mainly stable quotients of type-definable groups and invariant types in NIP theories. We extend the modelling property to continuous theories and use it to study $n$-dependence in hyperdefinable sets. Furthermore, we study maximal WAP and tame quotients of $S_X(\mathfrak{C})$, where $\mathfrak{C}$ is a monster model of a complete theory $T$ and $X$ is an $\emptyset$-type-definable set and show that the Ellis groups of the maximal WAP quotient flow and the maximal tame quotient flow do not depend on the choice of the monster model $\mathfrak{C}$.

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Adrián Portillo Fernández. 2024-12-19. Canonical quotients in model theory. https://arxiv.org/abs/2412.14862

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