Transitivity is a fundamental property of relations. If A relates to B, and B relates to C, then A must…
Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning,…
A non-standard model adheres to a theory's axioms but possesses unintended properties. It's crucial for demonstrating a theory's consistency and…
Negation consistency ensures a logical system is free from contradictions, meaning no statement and its negation can both be proven…
Negation completeness signifies a logical system's ability to prove either any given statement or its negation. This ensures that no…
A model in logic and mathematics interprets the symbols of a formal language, satisfying the axioms and theorems of a…
Metatheory involves the theoretical analysis of mathematical and logical systems. It examines properties, structure, and foundational aspects, providing a meta-level…
A metatheorem is a theorem that describes properties of a formal system, such as consistency or completeness. It operates on…
Metamathematics examines mathematical systems and theories from an elevated viewpoint, employing principles of mathematical logic. It explores the foundations and…
Metalogic explores the inherent properties of formal logical systems and languages. It investigates crucial aspects such as consistency, completeness, and…