constructive mathematics

Weak Excluded Middle in Intuitionistic Logic

The weak excluded middle asserts that for any proposition P, either P or not-P is provable. This differs from classical…

4 days ago

Weak Counterexample in Intuitionistic Logic

A weak counterexample in intuitionistic logic signifies a lack of positive evidence for an instance of the law of excluded…

4 days ago

Strong Counterexample in Intuitionistic Logic

A strong counterexample in intuitionistic logic disproves an instance of the law of excluded middle. It's a proof of negation,…

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Peirce’s Law

Peirce's law, ((P → Q) → P) → P, is a fundamental principle in logic. It is valid in classical…

4 days ago

Markov’s Principle

Markov's Principle, a cornerstone of constructive mathematics, asserts that if a property is impossible to lack, then an object possessing…

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Intuitionistic Mathematics

Mathematics built on intuitionistic logic, prioritizing constructive proofs and avoiding non-constructive axioms like the law of excluded middle. It emphasizes…

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Glivenko’s Theorem

Glivenko's theorem in logic connects classical and intuitionistic systems. It states that any formula provable in classical logic is also…

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Finitary Arithmetic

Finitary arithmetic is a mathematical approach that emphasizes constructive methods, avoiding infinite concepts. It focuses on operations and proofs that…

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Constructive Mathematics

Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…

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Brouwerian Modal Logic

A modal logic inspired by L.E.J. Brouwer's intuitionism. It grounds possibility in constructivist mathematics, offering a unique perspective on necessity…

4 days ago