Linked from

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

• SetRelated: Set theory is commonly axiomatized and studied using first-order formulas.

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

• Predicate logicBroader topic: It is the most widely used form of predicate logic, quantifying over objects in a domain.

• Propositional logicCompared with: It extends propositional reasoning with quantification and relations among objects.

• AxiomRelated: Many mathematical axioms are expressed and studied in first-order logic.

• Classical logicBroader topic: It extends classical propositional reasoning to quantified statements.

• Automated theorem provingRelated: Many theorem provers target its expressive language and inference rules.

• Aristotelian logicCompared with: It generalizes categorical reasoning with explicit quantification and relations of arbitrary complexity.

• Gödel numberingRelated: Its formulas and proof rules are among the main objects encoded in mathematical logic.

• Mathematical logicBroader topic: It is a central framework for expressing mathematical theories and proving statements about structures.

• Alonzo ChurchRelated: Church studied its formal systems and proved a major limit on their decision procedures.

• Kurt GödelRelated: First-order theories provide a standard setting for stating arithmetic and its axioms.

• 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.

• Modal logicCompared with: It adds quantification rather than modal operators, though modal predicate logics combine both.

• Peano arithmeticRelated: Standard Peano arithmetic uses first-order quantifiers to state properties of natural numbers.

• 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.

• Symbolic artificial intelligenceBroader topic: It expresses relationships and general rules more precisely than propositional logic.

• QuantifierRelated: Its standard quantifiers range over the domain’s individual objects.

• 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.

• Second-order logicCompared with: It provides the baseline that second-order quantifiers extend.

• 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.

• Axiom of extensionalityRelated: The axiom is commonly stated as a universally quantified formula in this logic.

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

• LogicismBroader topic: Fregean logicism uses quantified predicates to express mathematical relations and definitions.

• Axiom of pairingRelated: The axiom is expressed as a quantified sentence in this language.

• CompletenessBroader topic: Gödel's completeness theorem concerns its semantic consequence relation.

• Consistency proofRelated: Many consistency results are stated for theories formulated in this logic.

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

• Independence (mathematical logic)Related: Many standard independence results are stated for sentences in first-order theories.

• LogicBroader topic: It expresses quantified claims while keeping quantification restricted to individuals.

• Nonstandard analysisRelated: The transfer principle applies to first-order statements in the chosen mathematical language.

• Undecidable problemRelated: Validity in full first-order logic is undecidable, despite its precise formal rules.

• 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.

• Axiom schemaRelated: In first-order theories, schemas often express principles unavailable as single first-order sentences.

• 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.