A non-standard model adheres to a theory's axioms but possesses unintended properties. It's crucial for demonstrating a theory's consistency and…
Quine's New Foundations is a set theory designed to bypass paradoxes of naive set theory. It uses a unique axiom…
The set of positive integers, often denoted by N, typically including zero. Natural numbers form the foundation for counting, ordering,…
An n-ary relation connects 'n' elements, generalizing binary relations. It's fundamental in mathematics and computer science for describing complex relationships…
A monomorphism is a left-cancellable morphism in category theory. If f ∘ g = f ∘ h, then g =…
Model theory is a branch of mathematical logic exploring the connections between formal languages and their meanings in mathematical structures.…
Mathematical logic is the study of logic within mathematical reasoning. It explores the formal properties of logical systems, proving theorems,…
Logicism is the philosophical view that mathematics is a branch of logic. Proponents believe all mathematical truths can be derived…
A logical paradox is a statement or set of statements that results in a contradiction or defies intuition. It often…
A specialized field of logic focusing on the properties, composition, and inversion of relations, and their interplay with logical operators.…