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True arithmetic

In mathematical logic, true arithmetic is the set of all true first-order statements about the arithmetic of natural numbers. This is the theory associated with the standard model of the Peano axioms in the language of the first-order Peano axioms. True arithmetic is occasionally called Skolem arithmetic, though this term usually refers to the different…

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Overview

Definition

Arithmetic undefinability

Computability properties

Model-theoretic properties

True theory of second-order arithmetic

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True arithmetic

Nodes39
Edges38
Triples12
Avg. degree1.95
Density0.051282
Components1

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True arithmetic

Top relations

related to Arithmetic undefinability · 7
True arithmetic → Alfred Tarski, Gödel, Here, It, Th, The, This
related to Model-theoretic properties · 3
True arithmetic → As, Since, True
is a · 2
True arithmetic → set of all true first-order statements about the arithmetic of natural numbers, undefinability theorem of Alfred Tarski

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Important terminology

arithmetic displaystyle mathcal true theory first-order th language theorem logic set signature structure sentence natural second-order isbn models definable degrees

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
True arithmeticis aset of all true first-order statements about the arithmetic of natural numbers0.90text
True arithmeticis aundefinability theorem of Alfred Tarski0.90text
True arithmeticrelated to Arithmetic undefinabilityThe0.60section
True arithmeticrelated to Arithmetic undefinabilityAlfred Tarski0.60section
True arithmeticrelated to Arithmetic undefinabilityIt0.60section
True arithmeticrelated to Arithmetic undefinabilityTh0.60section
True arithmeticrelated to Arithmetic undefinabilityThis0.60section
True arithmeticrelated to Arithmetic undefinabilityHere0.60section
True arithmeticrelated to Arithmetic undefinabilityGödel0.60section
True arithmeticrelated to Model-theoretic propertiesTrue0.60section
True arithmeticrelated to Model-theoretic propertiesAs0.60section
True arithmeticrelated to Model-theoretic propertiesSince0.60section

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    Min side: 3
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