About: Non-standard model of arithmetic

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In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934).

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rdf:type	person
rdfs:label	Non-standard model of arithmetic (en)
rdfs:comment	In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). (en)
sameAs	Non-standard model of arithmetic Non-standard model of arithmetic
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Subject	Arithmetic Mathematical logic Model theory Formal theories of arithmetic
gold:hypernym	Model
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic?oldid=1065881675&ns=0
Wikipage page ID	6251420 (xsd:integer)
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Wikipage revision ID	1065881675 (xsd:integer)
Link from a Wikipage to another Wikipage	Nonstandard analysis Ultraproduct Proof that 22/7 exceeds π Semiring Thoralf Skolem Upper set Ω-consistent theory Cardinality Arithmetic George Boolos Mathematical logic Model theory Second-order logic Zermelo–Fraenkel set theory Dense order Hyperinteger Tennenbaum's theorem Compactness theorem Computability theory Countable set Order type First-order logic Fundamenta Mathematicae Goodstein's theorem Formal theories of arithmetic Gödel's completeness theorem Gödel's incompleteness theorems Peano axioms Stanley Tennenbaum Total order Isomorphism Löwenheim–Skolem theorem Mathematical logic Rational number Richard Jeffrey
has abstract	In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic
is Wikipage redirect of	Non-standard number Nonstandard model of arithmetic Non-standard arithmetic Non-standard integers Non-standard number theory Nonstandard arithmetic Nonstandard models of arithmetic Nonstandard number theory
is Link from a Wikipage to another Wikipage of	Non-standard model Non-standard number Nonfirstorderizability Nonstandard integer Nonstandard model of arithmetic Non-standard arithmetic Non-standard integers Non-standard number theory Nonstandard arithmetic Nonstandard models of arithmetic Nonstandard number theory Hyperinteger List of mathematical logic topics Elementary equivalence Finite model theory Goodstein's theorem Karen Yeats Gödel's completeness theorem Gödel's incompleteness theorems Induction, bounding and least number principles Mathematical logic History of numbers

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