Satisfiable Theory

Last updated Nov 1, 2022

Let $\mathcal{L}$ be a Language and let $T$ be an $\mathcal{L}$-Theory. We say $T$ is a Satisfiable Theory if there is an $\mathcal{L}$-Language Structure $\mathcal{M}$ such that $\mathcal{M} \models T$.

1. Let $\mathcal{L} = {0}$. Here is an example of an $\mathcal{L}$-Theory that is not a Satisfiable Theory: $$T = {x = 0, \neg(x = 0)}.$$ The two Sentences are contradictory, so it has no Model.

• Model