The weak excluded middle asserts that for any proposition P, either P or not-P is provable. This differs from classical…
A weak counterexample in intuitionistic logic signifies a lack of positive evidence for an instance of the law of excluded…
A strong counterexample in intuitionistic logic disproves an instance of the law of excluded middle. It's a proof of negation,…
Peirce's law, ((P → Q) → P) → P, is a fundamental principle in logic. It is valid in classical…
Markov's Principle, a cornerstone of constructive mathematics, asserts that if a property is impossible to lack, then an object possessing…
Mathematics built on intuitionistic logic, prioritizing constructive proofs and avoiding non-constructive axioms like the law of excluded middle. It emphasizes…
Glivenko's theorem in logic connects classical and intuitionistic systems. It states that any formula provable in classical logic is also…
Finitary arithmetic is a mathematical approach that emphasizes constructive methods, avoiding infinite concepts. It focuses on operations and proofs that…
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…
A modal logic inspired by L.E.J. Brouwer's intuitionism. It grounds possibility in constructivist mathematics, offering a unique perspective on necessity…