Strong completeness in logic means that if a formula is true in all interpretations (semantically valid), it can be proven…
A theory is Post consistent if it contains at least one unprovable statement. If all statements are provable, the theory…
Löb's theorem in mathematical logic states that if a system can prove that a statement implies its own provability, then…
Mathematics built on intuitionistic logic, prioritizing constructive proofs and avoiding non-constructive axioms like the law of excluded middle. It emphasizes…
An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…
A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…
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…
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…
Cardinal numbers represent the quantity or size of a set. They answer the question 'how many?' and form the basis…