A finitary formal system uses only finite operations, proofs, and expressions. It relies on objects constructible in a finite number…
Finitary arithmetic is a mathematical approach that emphasizes constructive methods, avoiding infinite concepts. It focuses on operations and proofs that…
An endomorphism is a structure-preserving function mapping a mathematical object to itself. It's a fundamental concept in abstract algebra, category…
A technique in mathematical logic to remove quantifiers from formulas, preserving logical equivalence. Crucial in theories like real closed fields…
A crucial lemma in Gödel's incompleteness theorems. It states that for any formula with one free variable, there exists a…
Curry's paradox is a logical paradox that emerges from self-referential statements asserting their own unprovability. It challenges the consistency of…
A constructive proof shows a mathematical object exists by providing a method to build it. This contrasts with indirect proofs,…
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…
Constructive logic emphasizes explicit proofs of existence, demanding a concrete construction rather than indirect reasoning. It's a foundational approach in…
Combinatory logic is a branch of mathematical logic that aims to simplify mathematical expressions by replacing variables with combinators. It…