First-order variables are placeholders for individuals within a specific domain in first-order logic. They are fundamental to expressing general statements…
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships between individuals, properties, and relations, forming the foundation…
First-order logic (FOL) is a formal system using quantifiers like 'for all' and 'there exists' to reason about individuals. It's…
Finite model theory explores structures with finite domains. It investigates properties and expressiveness of logical languages within these finite settings,…
Elementary equivalence signifies that two structures share all the same first-order sentences. This concept is crucial in model theory for…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…
A fundamental theorem in mathematical logic asserting that if every finite subset of a set of sentences is satisfiable, then…