Let us consider the language consisting of one symbol $R$ for a binary relation. Let $\sigma$ denote the following sentence:

$\forall x \exists y \exists z \ x\neq y \wedge y \neq z \wedge x \neq z \wedge x R y \wedge z R x$.

Does $\sigma$ have a finite model? I know that if $S$ is an interpretation structure for a set of formulas $\Gamma$, $S$ is called a model for $\Gamma$, written $S \models \Gamma$, if all the formulas in $\Gamma$ are true in $S$. How would I show this? Thanks


HINT: Think of a triangle whose vertices represent the points of the model, and whose edges represent the relation $R$.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.