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Peano axioms

In mathematical logic, the Peano axioms (/piˈɑːnoʊ/; ), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental…

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Historical second-order formulation

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Peano arithmetic as first-order theory

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Historical second-order formulation

Peano arithmetic as first-order theory

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Peano axioms

Nodes138
Edges137
Triples120
Avg. degree1.99
Density0.014493
Components1

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Peano axioms

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related to External links · 42
Peano axioms → Archived, Around, Bradley, Burris, Commentary, Creative Commons Attribution/Share-Alike License, Dedekind, Dedekind's, Dowden, EMS Press, Encyclopedia, Eric, First Order Arithmetic, Gödel's Theorem, Henri Poincaré, In Fieser, Includes, Internet Encyclopedia, ISSN, James
related to Consistency · 18
Peano axioms → Although, Bertrand Russell, David Hilbert, Gentzen, Gentzen's, Gerhard Gentzen, Gödel, Gödel's, Henri Poincaré, Hilbert, In, Kurt Gödel, Peano, Peano's, The, Turing, When, Whether
related to Models · 15
Peano axioms → Dedekind, German, In, Meaning, NA, NB, Numbers, Peano, SA, SB, The Nature, This, Was, What, Zahlen
related to Nonstandard models · 11
Peano axioms → Although, Dedekind's, In, Löwenheim, PA, Peano, Skolem, The, This, When, ZFC
related to Historical second-order formulation · 10
Peano axioms → Begriffsschrift, Boole, Frege's, Gottlob Frege, Peano, Peano's, Schröder, The, The Peano, When Peano
related to Peano arithmetic as first-order theory · 9
Peano axioms → All, As, First-order, In, Peano, Such, The, Therefore, Thus
related to Responses and reactions · 8
Peano axioms → Another, Bertrand Russell, For, His, Introduction, Mathematical Philosophy, Peano, Peano's
related to Defining arithmetic operations and relations · 4
Peano axioms → However, If, Peano, The
is a · 1
Peano axioms → triple

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axioms natural peano numbers first-order arithmetic addition induction displaystyle multiplication number axiom pa second-order set theory successor model one forall

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Peano axiomsis atriple0.90text
ZFinstance ofThe Peano axioms can be derived from set theoretic constructions of the natural numbers and axioms of set theory0.80text
Gentzen's proofinstance ofrelying either on intuition or the acceptance of a consistency proof0.80text
Peano axiomsrelated to ConsistencyWhen0.60section
Peano axiomsrelated to ConsistencyPeano0.60section
Peano axiomsrelated to ConsistencyBertrand Russell0.60section
Peano axiomsrelated to ConsistencyHenri Poincaré0.60section
Peano axiomsrelated to ConsistencyIn0.60section
Peano axiomsrelated to ConsistencyDavid Hilbert0.60section
Peano axiomsrelated to ConsistencyKurt Gödel0.60section
Peano axiomsrelated to ConsistencyAlthough0.60section
Peano axiomsrelated to ConsistencyGödel's0.60section

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