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Topological modal logic of \(\mathbb R\) with inequality. (English. Russian original) Zbl 1185.03033

Russ. Math. Surv. 63, No. 1, 163-165 (2008); translation from Usp. Mat. Nauk. 63, No. 1, 163-164 (2008).
A topological semantics for the difference modality \(D\) is given by: \(M,x\models DA\) iff \((\forall y\not=x)M,y\models A\). The author proves that the \(\square,D\)-logic of the real line \(\mathbb{R}\) is not finitely axiomatizable.

MSC:

03B45 Modal logic (including the logic of norms)
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