Simulation of two dimensions in unimodal logics

In this paper, we prove undecidability and the lack of finite model property for a certain class of unimodal logics. To do this, we adapt the technique from the paper “Products of ‘transitive’ modal logics” by D. Gabelaia, A. Kurucz, F. Wolter and M. Zakharyaschev (2005), where products of transitive modal logics were investigated, for the unimodal case. As a particular corollary, we present an undecidable unimodal fragment of Halpern and Shoham's Interval Temporal Logic.