Compactness: A set of sentences has a model iff every finite subset does. Löwenheim-Skolem: If a countable theory has an infinite model, it has models of every infinite cardinality.
Model Theory
Field: Mathematical Logic
The study of model theory.
Sequence of Expressions
Theorem
AdvancedCompleteness Theorem
In first-order logic, every logically valid formula is provable.
Definition
Model Theory (Definition)
It studies structures that satisfy sets of sentences in a formal language.