 Recall that the Kripke construction starts with a classical language \(\mathcal{L}_0\) with no truth predicate. It passes to an expanded language \(\mathcal{L}^{+}_0\), but unlike a Tarskian metalanguage, this language contains a truth predicate \(\Tr\) that applies to all of \(\mathcal{L}^{+}_0\). Kripke shows how to build a partial interpretation of \(\Tr\), providing an extension \(\mathcal{E}\) and an anti-extension \(\mathcal{A}\). But one can then simply consider the classical model \(\langle \mathcal{M}_0,\mathcal{E}\rangle\), using only the extension. This is the ‘closed-off’ construction, as the gap between extension and anti-extension is closed off by throwing everything in the gap into the false category of a classical model.