On first-order expressibility of satisfiability in submodels

Denis I. Saveliev

Let $\kappa ,\lambda$ be regular cardinals, $\lambda \le \kappa$, let $\phi$ be a sentence of the language ${\mathcal{L}}_{\kappa ,\lambda }$ in a given signature, and let $\vartheta (\phi )$ express the fact that $\phi$ holds in a…