For a formula $ \gamma = r \leftrightarrow (p_1 \vee p_2) $ there is true that: $\rho \models \gamma $ iff $\rho(r) = \max(\rho(p_1), \rho(p_2))$
Is there exists such set of formulas $\Gamma$ that $\rho \models \Gamma$ iff $\rho(r) = \max_{n \in \mathbb{N}} (\rho(p_n))$ where $\rho$ is a vaulation.
Do I understand correctly that I should prove that there exists expected set that it is true $\rho(r) = \max_{n \in \mathbb{N}} (\rho(p_n))$ for any $r$?
$\rho \models \gamma $ means that $\rho$ satisfies $\gamma$
If yes, please hint me If no, please explain what I should do.