Linked from

The 75 pages that link to First-order logic, each with the reason it gives.

• Model theoryNarrower topic: Its languages provide the standard syntax whose interpretations model theory studies.

• Compactness theoremNarrower topic: The theorem applies to sets of sentences in this logic.

• Alfred TarskiNarrower topic: Its languages and structures provide the setting for Tarski’s accounts of truth and logical consequence.

• EntscheidungsproblemNarrower topic: The Entscheidungsproblem asks for a validity test covering every statement in this logic.

• Interpretation (logic)Narrower topic: Its symbols and formulas are the standard setting in which interpretations are defined.

• Existential quantificationNarrower topic: Existential quantification is one of its two standard quantifiers.

• Free variableNarrower topic: Its formulas use free variables to express claims relative to assignments.

• Universal quantificationNarrower topic: Universal quantification is a basic operator in first-order logic.

• Domain of discourseNarrower topic: Its interpretations specify the domain over which quantified variables range.

• Hoare logicNarrower topic: Its predicates and quantifiers often express program assertions.

• Gödel's completeness theoremNarrower topic: The theorem establishes a correspondence between this logic's semantics and proof rules.

• Diagonal lemmaNarrower topic: The lemma is stated for formulas and sentences in a formal language.

• Gödel's constructible universeNarrower topic: Definability at each stage uses first-order formulas interpreted in set-sized structures.

• Löwenheim–Skolem theoremNarrower topic: The theorem's model-size flexibility is a characteristic limitation of first-order expression.

• Presburger arithmeticNarrower topic: Presburger arithmetic uses quantifiers and logical connectives to state its formulas.

• Peano axiomsNarrower topic: The standard first-order formulation expresses the axioms using this logic.

• Membership relationNarrower topic: Set theory represents membership as a binary predicate within a logical language.

• PredicateNarrower topic: It supplies the standard formal language in which predicates are interpreted.

• Categorical theoryNarrower topic: The classical notion of categoricity concerns models of first-order theories.

• Elementary equivalenceNarrower topic: Its sentences provide the tests that two structures must agree on.

• Giuseppe PeanoNarrower topic: Peano’s logical work helped develop formal systems for expressing mathematics.

• Arithmetical hierarchyNarrower topic: Its existential and universal quantifiers form the patterns that distinguish hierarchy levels.

• DatalogNarrower topic: Datalog draws on logical rules while restricting syntax to support effective computation.

• Gödel sentenceNarrower topic: Gödel sentences are formulated inside theories expressed in a formal language such as this.

• Prenex normal formNarrower topic: Prenex form is a normal form for formulas in this logic.

• Von Neumann–Bernays–Gödel set theoryNarrower topic: NBG’s axioms are expressed in a first-order language with class and set variables.

• Axiom schema of replacementNarrower topic: Each instance of replacement is expressed as a first-order axiom in the language of set theory.

• Description logicNarrower topic: Description logics draw on predicate logic while restricting syntax to preserve useful reasoning properties.

• Tarski's axiomsNarrower topic: Tarski's axioms quantify over points and state properties of their betweenness and congruence.

• Atomic formulaNarrower topic: Atomic formulas are the quantifier-free base cases in first-order formula construction.

• Herbrand's theoremNarrower topic: Herbrand's theorem links its quantified formulas to propositional reasoning.

• Skolem normal formNarrower topic: Skolem normal form is defined for formulas in this logic.

• Lindenbaum's lemmaNarrower topic: In first-order logic, the lemma extends consistent theories in a language with quantifiers.

• Löb's theoremNarrower topic: Löb’s theorem is formulated within formal systems whose reasoning can be represented logically.

• Jaakko HintikkaNarrower topic: Hintikka’s work on quantification and its limits begins from this central logical system.

• Trakhtenbrot's theoremNarrower topic: The theorem identifies a boundary between finite and unrestricted models of this logic.

• Universe (mathematics and logic)Narrower topic: Its quantifiers range over a specified domain rather than over arbitrary properties.