Equivalent Formulas

Last updated Nov 1, 2022

Let $\mathcal{L}$ be a Language. Two $\mathcal{L}$-Formulas $\phi, \psi$ are Equivalent Formulas if $$\mathcal{M } \models_{\sigma} \phi \Leftrightarrow \mathcal{M} \models_{\sigma} \psi$$ for any $\mathcal{L}$-structure $\mathcal{M}$ and any Assignment $\sigma$.