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arXiv · 2405.03785

On the Model Theory of Second-Order Objects

Tapani Hyttinen·Joni Puljujärvi·Davide Emilio Quadrellaro
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Abstract

Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that generalizes the standard notion of abstract elementary class, and show that it is an example of an accessible category. We apply our framework to show that the logic $\mathsf{FOT}$ introduced by Kontinen and Yang satisfies a version of Lindström's Theorem. Finally, we consider the problem of transferring categoricity between different cardinalities for complete theories in existential second-order logic (or independence logic) and prove both a downwards and an upwards categoricity transfer result.

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Tapani Hyttinen, Joni Puljujärvi, Davide Emilio Quadrellaro. 2026-05-07. On the Model Theory of Second-Order Objects. https://arxiv.org/abs/2405.03785

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