Временная логика линейных по времени фреймов с аксиомой индукции

A class of frames based on a class of frames with discrete linear time with current time point clusters is considered. The temporal calculus $\mathbf{LInd}$ is found which is complete with respect to this class. It is proved that $\mathbf{LInd}$ has the finite model property and therefore it is decidable.