INCLUSION CRITERIA
An entry belongs in this subdivision if and only if its subject is the model theory of a logic—the structures satisfying its formulas, their construction and classification, or the definability of properties over them.
Required: At least one of the following:
- A theorem or technique about satisfaction, definability, or elementary classes (compactness, LS, interpolation, ultraproducts, QE, stability)
- A method of constructing or comparing models (forcing, inner models, saturation, embeddings)
- A model-theoretic characterization of expressive power (descriptive complexity, abstract model theory, the team-semantic analysis of expressiveness)
Not sufficient: A named logic evaluated on teams rather than on assignments (that belongs in Team; the semantics as a technique is cross-listed here). A named logic built on truthmaker or state-based semantics (that belongs in Hyperintensional; the semantics as a technique is cross-listed here). A proof calculus or a result about derivations (Proof-Systems). A category-theoretic semantics (Categorical). A theory of computability or degrees (Computability).
Boundary: Model-theoretic semantics of natural language is cross-listed with Applications/Semantics. Descriptive complexity is cross-listed with Proof-Systems (proof complexity) where the two meet. Tarski's undefinability of truth lives here; Gödel's incompleteness (a fact about provability) lives in Proof-Systems.