model theory

Downward Löwenheim–Skolem Theorem

The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…

5 days ago

Double Turnstile Symbol (⊨) in Logic

The double turnstile (⊨) symbol signifies semantic entailment or logical consequence. It indicates that the truth of certain propositions guarantees…

5 days ago

Compactness Theorem

A fundamental theorem in mathematical logic asserting that if every finite subset of a set of sentences is satisfiable, then…

5 days ago

Categorical Theories in Mathematics

A categorical theory ensures all its models are isomorphic. This means different representations describe the same underlying mathematical structure, providing…

5 days ago

Branching Quantifiers in Formal Logic

Branching quantifiers express complex dependencies between quantified variables, going beyond linear quantification. They allow for more intricate logical relationships and…

5 days ago