$\Sigma_1$-Stationary logic as an $\aleph_1$-Abstract Elementary Class

Will Boney

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arXiv · 2410.23967

$\Sigma_1$-Stationary logic as an $\aleph_1$-Abstract Elementary Class

Will Boney

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Abstract

$\mu$-Abstract Elementary Classes are a model theoretic framework introduced in [BGL+16] to encompass classes axiomatized by $\mathbb{L}_{\infty, \infty}$. We show that the framework extends beyond these logics by showing classes axiomatized in $\mathbb{L}(aa)$ with just the $aa$ quantifier are an $\aleph_1$-Abstract Elementary Class.

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Will Boney. 2024-10-31. $\Sigma_1$-Stationary logic as an $\aleph_1$-Abstract Elementary Class. https://arxiv.org/abs/2410.23967

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