Semantically Equivalent Terms are Equal

Theorem

Let $\tau_1, \tau_2$ be terms.

Suppose that they are semantically equivalent with respect to the empty set.

Then $\tau_1 = \tau_2$.

Proof

This theorem requires a proof. In particular: While an exercise, this basically requires construction of the syntactic model in order to achieve full rigour You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.8$ Further Semantic Notions: Exercise $\mathrm{II.8.5}$