$\hat{I}{\pounds }_1$-Stationary logic as an ${\aleph }_1$-Abstract Elementary Class

Abstract

$\hat{I}¼$-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.