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arXiv · 1801.01908

Structural Logic and Abstract Elementary Classes with Intersection

Will Boney·Sebastien Vasey
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Abstract

We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structural logic: we prove that AECs with intersections correspond to classes of models of a universal theory in structural logic. This generalizes Tarski's syntactic characterization of universal classes. As a corollary, we obtain that any AEC with countable Löwenheim-Skolem number is axiomatizable in $\mathbb{L}_{\infty, ω} (Q)$, where $Q$ is the quantifier "there exists uncountably many".

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BibTeXRIS

Will Boney, Sebastien Vasey. 2018-12-09. Structural Logic and Abstract Elementary Classes with Intersection. https://doi.org/10.4064/ba8178-12-2018

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