The aim of this paper is to study the restriction of a tent map $f\colon I\to I$ to a subinterval $J\subset I$, and to characterize when the maximal invariant of $f|_J$ is a countable set. We shall extend our results for a certain class of unimodal maps, via a semi-conjugacy. In the case of tent maps there is a critical case where the maximal invariant set is a Cantor set with Hausdorff dimension zero. The caracterization of this critical case leads to interesting arithmetical phenomena, particularly in the case of the complete tent map.