It is a well-known fact that the intuitionistic propositional logic is complete with respect to the class of all Heyting algebras. The mentioned theorem by A. Tarski [Fundam. Math. 31, 103–134 (1938; Zbl 0020.33704)] states that this logic is complete w.r.t. to all Heyting algebras \(O(X)\) of open sets of a topological space \(X\): every non-theorem is falsified by some \(O(X)\). Actually, the class of admissible spaces here can be considerably restricted: for example, \(X\) may be any Euclidean space \(R^n\). This means, in particular, that the Heyting algebras \(O(R^n)\) and \(O(R^M)\) with \( m \neq n\) satisfy the same formulas; consequently, the intuitionistic logic cannot detect the topological dimension of an Euclidean space. Another classical result on intitionistic logic, which goes back to a short note in 1936 by S. Jaskowski [Actual. Sci. Ind. 393, 58–61 (1936; JFM 62.1045.07)], saying that the logic has the finite model property: a non-theorem can be falsified by a finite Heyting algebra. In the paper under review, the authors provide a Tarski style theorem that uses only locally finite Heyting algebras of open sets, and hence covers also Jaśkowski’s theorem [loc. cit.]. Namely, they consider the lattice of open subpolyhedra of a compact polyhedron \(P \subseteq R^n\), which turns out to be a locally finite Heyting subalgebra of \(O(P)\), and show that the intuitionistic logic is the logic of formulas valid just in all Heyting algebras arising in this way. They also show that the logic is able, in a sense, to capture the topological dimension of a polyhedron.