KnowraPeano arithmeticLinked fromLinked fromThe 18 pages that link to Peano arithmetic, each with the reason it gives.All 18Broader topic 5Related 9Compared with 4Natural numberRelated: It turns familiar operations on natural numbers into a system for mathematical proof.Diagonal lemmaRelated: It can formalize the coding operations needed for the standard arithmetic form of the lemma.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.Gödel's first incompleteness theoremRelated: The concrete system the theorem applies to, with explicit independent sentences.