Linked from

The 18 pages that link to Peano arithmetic, each with the reason it gives.

• Gödel's incompleteness theoremsBroader topic: The concrete theory to which the theorems apply; it is incomplete if consistent.

• Natural numberRelated: It turns familiar operations on natural numbers into a system for mathematical proof.

• Kurt GödelBroader topic: Gödel encoded statements about proofs within arithmetic of this kind.

• EntscheidungsproblemCompared with: Its theorem set is undecidable, a related limit distinct from first-order validity itself.

• Interpretation (logic)Broader topic: Its intended interpretation uses natural numbers, while other structures can satisfy its axioms too.

• DecidabilityCompared with: Unlike Presburger arithmetic, the set of its theorems is not decidable.

• Diagonal lemmaRelated: It can formalize the coding operations needed for the standard arithmetic form of the lemma.

• Presburger arithmeticCompared with: Unlike Presburger arithmetic, it includes variable multiplication and is incomplete and undecidable.

• Peano axiomsBroader topic: It develops the first-order Peano axioms into an arithmetic theory.

• Axiom schemaRelated: Its induction schema provides a familiar example of infinitely many arithmetic axioms.

• Goodstein's theoremRelated: Goodstein's theorem is true but has no proof in this theory.

• Ordinal analysisRelated: Its proof-theoretic ordinal is a standard benchmark for analyzing arithmetic theories.

• Arithmetical hierarchyRelated: Its formulas provide a setting for studying definability and provability across quantifier levels.

• Gödel sentenceRelated: It is a standard setting rich enough to encode its own formulas and proofs.

• Paris–Harrington theoremRelated: The theorem’s natural-number statement cannot be proved in this theory.

• Löb's theoremBroader topic: It is a standard example of a sufficiently strong theory for arithmetized provability.

• Gödel's first incompleteness theoremRelated: The concrete system the theorem applies to, with explicit independent sentences.

• Kruskal's tree theoremCompared with: The full theorem is not provable in this standard arithmetic theory.