Find $K\subseteq \operatorname{Ass} $ and $ K'\subseteq K$ such that $K$ is definable but $K'$ is not.
Definition (Definable): a set $K$ of assignments is definable if there is a set of formulas A such that $\operatorname{Ass}(A) = K$.
2026-04-18 13:29:51.1776518991
Find indefinable set that is included in definable set.
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Hint: $K=\mathit{Ass}$ is definable, so all you need to do is find some non-definable set of assignments.
You need to involve infinitely many propositional variable, because every truth functional of finitely many variables can be defined by a single formula.
How about the set of all possible assignments except the one that makes every propositional variable false?