202504050604

Tags : Finite Model Theory

Finitely Satisfiable and Valid Sentences

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Definition

Given a vocabulary $\sigma$, a sentence $\Phi$ in that vocabulary is called Finitely Satisfiable if there a finite structure $\mathcal{A}$ such that $\mathcal{A}\models \Phi$. A sentence $\Phi$ is called Finitely Valid for all finite structures $\mathcal{A}\in \text{STRUCT}[\sigma ]$, we have $\mathcal{A}\models \Phi$

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References