Remarks on Shelah's classification theory and Quillen's negation

Misha Gavrilovich

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arXiv · 2010.08791

Remarks on Shelah's classification theory and Quillen's negation

Misha Gavrilovich

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Abstract

We give category-theoretic reformulations of stability, NIP, NTP, and non-dividing by observing that their characterisations in terms of indiscernible sequences are naturally expressed as Quillen lifting properties %(negation) of certain morphisms associated with linear orders, in a certain category extending the categories of topological spaces and of simplicial sets. This suggests an approach to a homotopy theory for model theory.

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Misha Gavrilovich. 2020-10-17. Remarks on Shelah's classification theory and Quillen's negation. https://arxiv.org/abs/2010.08791

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