The Lattice of Extensions of the Modal Logic of Two Equivalence Relations Has the Cardinality of the Continuum / Izmailov M.M. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 4. P. 46-48 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
A continuum of different logics over S5×S5 is constructed. This proves that the cardinality of the lattice of all normal extensions of the logic of two equivalence relations Ext(S5×S5) is continuum.
modal logic, fusion of logics, extensions of logics,
logic of equivalence relation.