The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…
The double turnstile (⊨) symbol signifies semantic entailment or logical consequence. It indicates that the truth of certain propositions guarantees…
A fundamental theorem in mathematical logic asserting that if every finite subset of a set of sentences is satisfiable, then…
A categorical theory ensures all its models are isomorphic. This means different representations describe the same underlying mathematical structure, providing…
Branching quantifiers express complex dependencies between quantified variables, going beyond linear quantification. They allow for more intricate logical relationships and…