Separating Markov's Principles
Liron Cohen, Yannick Forster, Dominik Kirst, Bruno Da Rocha Paiva, Vincent Rahli · 2024
Markov's principle (MP) is an axiom in some varieties of constructive mathematics, stating that Σ01 propositions (i.e. existential quantification over a decidable predicate on N) are stable under double negation. However, there are various non-equivalent definitions of decidable predicates and thus Σ01 in constructive foundations, leading to non-equivalent Markov's principles. While this fact is well-reported in the literature, it is often overlooked, leading to wrong claims in standard references and published papers.