The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color

This theorem applies to "classical" mathematics (which is basically mathematics based on classical logic). But are there any mathematical systems based on different types of logic (e.g non classical logics) where this theorem would not hold? Since there are logics where fundamental principles of classical logic do not hold (e.g the law of excluded middle in intuitionistic logic), wouldn't it be the same for this theorem?