 Falling into neither the extension or the anti-extension of \(\Tr\) acts like having a third value, and we can interpret \(\mathcal{L}^{+}_0\) as acting like a language with a \(K_3\) valuation scheme. Treating the language this way, Kripke shows how to build up a very plausible extension and anti-extension for \(\Tr\), typically written \(\mathcal{E}\) and \(\mathcal{A}\). The important property of the new extended model \(\langle \mathcal{M}_0,\langle \mathcal{E},\mathcal{A}\rangle \rangle\) is that the truth value of any sentence \(A\) and \(\Tr(\left\ulcorner A\right\urcorner)\) are exactly the same. \(A\) is true, false, or neither, just in case \(\Tr(\left\ulcorner A\right\urcorner)\) is. Furthermore, interpreting the expanded language \(\mathcal{L}^{+}_0\) as a \(K_3\) language, we have for \(K_3\) consequence \(A \dashv \vdash \Tr(\left\ulcorner A\right\urcorner)\), just as we desired.