Linked from

The 53 pages that link to Model theory, each with the reason it gives.

• Predicate logicRelated: It studies which structures make predicate-logic sentences true.

• AxiomRelated: It asks which structures satisfy a theory's axioms.

• Logical consequenceNarrower topic: Models provide the structures used to define semantic consequence.

• Proof theoryCompared with: It investigates interpretation and truth in structures, complementing proof-centered analysis.

• ConsistencyRelated: A model of a theory can establish its consistency when the soundness of the proof system is known.

• Mathematical logicBroader topic: It gives semantics to formal theories and studies which structures make their axioms true.

• SoundnessNarrower topic: It supplies the models against which proved statements are checked.

• Compactness theoremNarrower topic: Compactness is one of model theory's central structural theorems.

• Alfred TarskiBroader topic: Tarski established core methods and results that helped make this field a distinct discipline.

• Formal systemNarrower topic: It examines what axioms mean when interpreted in mathematical structures.

• Interpretation (logic)Related: It investigates which interpretations make sets of sentences true.

• Logical equivalenceNarrower topic: It supplies the interpretations over which semantic equivalence is defined.

• Formal logicBroader topic: It studies the structures in which logical formulas hold or fail.

• Foundations of mathematicsRelated: It connects axioms with the structures in which they hold.

• Free variableRelated: Satisfaction for formulas with free variables is defined relative to assignments.

• Universal quantificationNarrower topic: It explains universal formulas through truth across every object in a model.

• SatisfiabilityNarrower topic: Satisfiability is defined through structures that make sentences true.

• Axiomatic methodRelated: Models give semantic interpretations to axioms beyond their written form.

• FormalismRelated: It connects formal syntax to interpretations in which mathematical statements acquire truth values.

• Domain of discourseRelated: It compares structures with different domains to study the same theory.

• Formal semanticsNarrower topic: It supplies structures and satisfaction relations for interpreting logical languages.

• Gödel's completeness theoremNarrower topic: The theorem lets model-theoretic truth be analyzed through formal derivability.

• CompletenessNarrower topic: Models supply the interpretations used to define semantic consequence.

• Consistency proofNarrower topic: A model satisfying a theory provides a semantic route to proving consistency.

• Independence (mathematical logic)Related: Models of the axioms with opposite truth values can establish independence.

• Nonstandard analysisRelated: Model-theoretic constructions provide a rigorous route to nonstandard extensions.

• Löwenheim–Skolem theoremNarrower topic: The theorem is a foundational result about the range of models theories can have.

• Foundations of GeometryRelated: Models give precise interpretations in which geometric axioms can be tested.

• Philosophy of mathematicsRelated: Models connect formal axioms to possible mathematical structures and interpretations.

• Universal algebraCompared with: Model theory allows arbitrary first-order conditions, while universal algebra centers on operations and identities.

• Axiomatic systemNarrower topic: It examines which structures make the system's axioms true.

• Hilbert's axiomsRelated: Models reveal what structures satisfy Hilbert's axioms and whether assumptions are independent.

• History of logicRelated: It added semantic interpretations to the syntactic systems developed in modern logic.

• Mathematical structureRelated: It treats structures as interpretations of symbols and investigates their logical properties.

• Structure (mathematical logic)Narrower topic: Structures are the central semantic objects studied in model theory.

• Elementary equivalenceRelated: It studies how syntactic agreement relates to structural similarity.

• Ordinal analysisCompared with: It examines theories through their models, offering a different perspective on formal strength.

• Higher-order logicNarrower topic: It distinguishes interpretations in which higher-order quantifiers range over all or only some properties.

• Quantifier eliminationNarrower topic: Quantifier elimination is a central model-theoretic property of theories.

• Description logicRelated: Interpretations and models define when description-logic statements are true.

• Formal scienceRelated: It connects symbolic theories to the mathematical structures in which they hold.

• Tarski's axiomsNarrower topic: Tarski's axioms invite analysis of which point structures satisfy the same geometric sentences.

• Automated reasoningRelated: Models give semantic meaning to formulas and determine whether claims hold under an interpretation.

• Lindenbaum's lemmaNarrower topic: The lemma became a standard tool linking syntactic consistency to semantic models.

• Skolem's paradoxNarrower topic: Skolem's paradox is a consequence of how first-order theories admit models.

• Ax–Grothendieck theoremRelated: Ax's proof uses logical transfer between algebraically closed fields.

• Axiom (mathematics and logic)Related: Models show whether an axiom set can be satisfied and what it permits.

• Barbara H. ParteeRelated: Model-theoretic tools provide a precise account of how expressions receive interpretations.

• Lindström's theoremNarrower topic: Lindström's theorem arose within model theory's study of logic and structures.

• Monotonicity of entailmentRelated: In classical semantics, adding premises restricts the models, preserving truths shared by the original models.