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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.

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

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

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

• 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.

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

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

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

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

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

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

• 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.

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

• Paris–Harrington theoremRelated: The theorem’s arithmetic formulation is expressed in first-order logic.

• Automated reasoningRelated: It expresses general claims about objects and relations that reasoning systems can process.

• Willard Van Orman QuineRelated: Quine used first-order logic to clarify ontological commitment and formal theory.

• Axiom of Empty SetRelated: The axiom is commonly expressed as a sentence in first-order logic.

• Law of identityRelated: Its identity symbol lets the law be stated for objects within a formal language.

• Skolem's paradoxRelated: Its quantifiers range over the model's domain, not over external collections of subsets.

• Craig interpolationRelated: Craig interpolation applies to first-order logical consequence as well as other formal systems.

• Knowledge (artificial intelligence)Related: Its variables and predicates express relationships among entities.