Equivalents of disjunctive Markov's principle

Abstract

The purpose of this short note is to point out a rich source of natural equivalents of the weak semi-intuitionistic principle MP$^\vee$ in reverse constructive mathematics: many simple theorems from Euclidean geometry when read classically (for example with $<$ interpreted as $\leqslant$ and $\neq$) are equivalent to disjunctive Markov's principle MP$^\vee$. We give an example of this phenomenon.