STRONG COMPLETENESS OF S4 FOR ANY DENSE-IN-ITSELF METRIC SPACE

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Strong Completeness of S4 for any Dense-in-Itself Metric Space

In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarl...

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ژورنال

عنوان ژورنال: The Review of Symbolic Logic

سال: 2013

ISSN: 1755-0203,1755-0211

DOI: 10.1017/s1755020313000087