[[!redirects decidable universal quantifiers]] ## Contents ## * table of contents {:toc} ## Definition ## Given a [[decidable setoid]] $T$, a **decidable universal quantifier on $T$** is a function $\forall x.(-)(x):(T \to \mathbb{2}) \to \mathbb{2}$ with a term $$p:\prod_{P:T \to \mathbb{2}} \left(\prod_{t:T} P(t) = 1\right) \to (\forall x.P(x) \equiv 1) \times \left(\left(\prod_{t:T} P(t) = 1\right) \to \emptyset \right) \to (\forall.P(x) \equiv 0)$$ ## See also ## * [[booleans]] * [[decidable setoid]] * [[decidable existential quantifier]] category: not redirected to nlab yet