Forking independence from the categorical point of view

Michael Lieberman; Jiří Rosický; Sebastien Vasey

doi:10.1016/j.aim.2019.02.018

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arXiv · 1801.09001

Forking independence from the categorical point of view

Michael Lieberman·Jiří Rosický·Sebastien Vasey

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Abstract

Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we require a characterization suitable for work in $\mu$-abstract elementary classes, i.e. accessible categories with all morphisms monomorphisms) and expository (we hope, with this account, to make forking accessible - and useful - to a broader mathematical audience). In particular, we present an axiomatic definition of what we call a stable independence notion on a category and show that this is in fact a purely category-theoretic axiomatization of the properties of model-theoretic forking in a stable first-order theory.

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BibTeX RIS

Michael Lieberman, Jiří Rosický, Sebastien Vasey. 2018-01-26. Forking independence from the categorical point of view. https://doi.org/10.1016/j.aim.2019.02.018

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