ON FINITE-DIMENSIONAL SUPERINTUITIONISTIC LOGICS
S. K. Sobolev · Mathematics of the USSR-Izvestiya · 1977
A pseudoboolean algebra is called -dimensional if the lattice is not embeddable in as a lattice, where is the two-element lattice. A superintuitionistic logic is said to be -dimensional if the formula belongs to it. A logic is -dimensional if and only if it is approximable by -dimensional algebras. All finite-dimensional logics are complete relative to Kripke semantics. An example is given of a formula that generates a logic not approximable by finite-dimensional algebras. It is proved that for every , every finitely axiomatizable -dimensional logic containing the formula is decidable (already for there exist among such logics non-finitely-approximable ones). The proof uses the theory of finite automata on -sequences.Bibliography: 10 titles.