Modal logics of relations induced by Hamming distance

The talk is based on the joint paper with A. V. Kudinov and V. B. Shehtman.
We consider modal logics of sets of words with relations induced by the Hamming metric. We show that these logics are closely related to many-dimensional products of modal logics. We present results on (un)decidability, non-finite axiomatizability and completeness for these logics.