DBpedia – Linked Data Fragments

Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Second-order_arithmetic> ?p ?o }

• Second-order_arithmetic abstract "In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. It was introduced by David Hilbert and Paul Bernays in their book Grundlagen der Mathematik. The standard axiomatization of second-order arithmetic is denoted Z2.Second-order arithmetic includes, but is significantly stronger than, its first-order counterpart Peano arithmetic. Unlike Peano arithmetic, second-order arithmetic allows quantification over sets of numbers as well as numbers themselves. Because real numbers can be represented as (infinite) sets of natural numbers in well-known ways, and because second order arithmetic allows quantification over such sets, it is possible to formalize the real numbers in second-order arithmetic. For this reason, second-order arithmetic is sometimes called “analysis”.Second-order arithmetic can also be seen as a weak version of set theory in which every element is either a natural number or a set of natural numbers. Although it is much weaker than Zermelo-Fraenkel set theory, second-order arithmetic can prove essentially all of the results of classical mathematics expressible in its language.A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z2). Such subsystems are essential to reverse mathematics, a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength. Much of core mathematics can be formalized in these weak subsystems, some of which are defined below. Reverse mathematics also clarifies the extent and manner in which classical mathematics is nonconstructive.".
• Second-order_arithmetic wikiPageExternalLink 2272259.
• Second-order_arithmetic wikiPageExternalLink sosoa.
• Second-order_arithmetic wikiPageExternalLink Proofs%2BTypes.html.
• Second-order_arithmetic wikiPageID "3542454".
• Second-order_arithmetic wikiPageLength "26282".
• Second-order_arithmetic wikiPageOutDegree "96".
• Second-order_arithmetic wikiPageRevisionID "707783065".
• Second-order_arithmetic wikiPageWikiLink 0_(number).
• Second-order_arithmetic wikiPageWikiLink Addition.
• Second-order_arithmetic wikiPageWikiLink Axiom.
• Second-order_arithmetic wikiPageWikiLink Axiom_of_projective_determinacy.
• Second-order_arithmetic wikiPageWikiLink Binary_operation.
• Second-order_arithmetic wikiPageWikiLink Binary_relation.
• Second-order_arithmetic wikiPageWikiLink Borel_set.
• Second-order_arithmetic wikiPageWikiLink Cambridge_University_Press.
• Second-order_arithmetic wikiPageWikiLink Category:Formal_theories_of_arithmetic.
• Second-order_arithmetic wikiPageWikiLink Cauchy_sequence.
• Second-order_arithmetic wikiPageWikiLink Classical_mathematics.
• Second-order_arithmetic wikiPageWikiLink Constructive_proof.
• Second-order_arithmetic wikiPageWikiLink Continuous_function.
• Second-order_arithmetic wikiPageWikiLink David_Hilbert.
• Second-order_arithmetic wikiPageWikiLink Dialectica_interpretation.
• Second-order_arithmetic wikiPageWikiLink Domain_of_discourse.
• Second-order_arithmetic wikiPageWikiLink Equiconsistency.
• Second-order_arithmetic wikiPageWikiLink Existential_quantification.
• Second-order_arithmetic wikiPageWikiLink First-order_logic.
• Second-order_arithmetic wikiPageWikiLink Foundations_of_mathematics.
• Second-order_arithmetic wikiPageWikiLink Free_variables_and_bound_variables.
• Second-order_arithmetic wikiPageWikiLink Function_(mathematics).
• Second-order_arithmetic wikiPageWikiLink Gaisi_Takeuti.
• Second-order_arithmetic wikiPageWikiLink Grundlagen_der_Mathematik.
• Second-order_arithmetic wikiPageWikiLink Individual.
• Second-order_arithmetic wikiPageWikiLink Infinite_set.
• Second-order_arithmetic wikiPageWikiLink Infix.
• Second-order_arithmetic wikiPageWikiLink Injective_function.
• Second-order_arithmetic wikiPageWikiLink Integer.
• Second-order_arithmetic wikiPageWikiLink Mathematical_analysis.
• Second-order_arithmetic wikiPageWikiLink Mathematical_logic.
• Second-order_arithmetic wikiPageWikiLink Multiplication.
• Second-order_arithmetic wikiPageWikiLink Natural_number.
• Second-order_arithmetic wikiPageWikiLink Open_set.
• Second-order_arithmetic wikiPageWikiLink Order_theory.
• Second-order_arithmetic wikiPageWikiLink Ordinal_analysis.
• Second-order_arithmetic wikiPageWikiLink Paris–Harrington_theorem.
• Second-order_arithmetic wikiPageWikiLink Paul_Bernays.
• Second-order_arithmetic wikiPageWikiLink Peano_axioms.
• Second-order_arithmetic wikiPageWikiLink Perfect_set_property.
• Second-order_arithmetic wikiPageWikiLink Prefix.
• Second-order_arithmetic wikiPageWikiLink Presburger_arithmetic.
• Second-order_arithmetic wikiPageWikiLink Primitive_recursive_arithmetic.
• Second-order_arithmetic wikiPageWikiLink Property_of_Baire.
• Second-order_arithmetic wikiPageWikiLink Quantifier_(logic).
• Second-order_arithmetic wikiPageWikiLink Rational_number.
• Second-order_arithmetic wikiPageWikiLink Real_number.
• Second-order_arithmetic wikiPageWikiLink Recursion.
• Second-order_arithmetic wikiPageWikiLink Reverse_mathematics.
• Second-order_arithmetic wikiPageWikiLink Robinson_arithmetic.
• Second-order_arithmetic wikiPageWikiLink Second-order_logic.
• Second-order_arithmetic wikiPageWikiLink Set_theory.
• Second-order_arithmetic wikiPageWikiLink Skolem_normal_form.
• Second-order_arithmetic wikiPageWikiLink Springer_Science+Business_Media.
• Second-order_arithmetic wikiPageWikiLink Subset.
• Second-order_arithmetic wikiPageWikiLink Successor_function.
• Second-order_arithmetic wikiPageWikiLink System_F.
• Second-order_arithmetic wikiPageWikiLink Term_(logic).
• Second-order_arithmetic wikiPageWikiLink Turing_jump.
• Second-order_arithmetic wikiPageWikiLink Uniformization_(set_theory).
• Second-order_arithmetic wikiPageWikiLink Variable_(mathematics).
• Second-order_arithmetic wikiPageWikiLink Well-formed_formula.
• Second-order_arithmetic wikiPageWikiLink Woodin_cardinal.
• Second-order_arithmetic wikiPageWikiLink Zermelo–Fraenkel_set_theory.
• Second-order_arithmetic wikiPageWikiLinkText "-comprehension".
• Second-order_arithmetic wikiPageWikiLinkText "Second-order arithmetic".
• Second-order_arithmetic wikiPageWikiLinkText "analysis".
• Second-order_arithmetic wikiPageWikiLinkText "recursive comprehension".
• Second-order_arithmetic wikiPageWikiLinkText "second-order arithmetic".
• Second-order_arithmetic wikiPageWikiLinkText "second-order comprehension".
• Second-order_arithmetic wikiPageWikiLinkText "second-order induction".
• Second-order_arithmetic wikiPageUsesTemplate Template:Citation.
• Second-order_arithmetic wikiPageUsesTemplate Template:Main.
• Second-order_arithmetic wikiPageUsesTemplate Template:Reflist.
• Second-order_arithmetic subject Category:Formal_theories_of_arithmetic.
• Second-order_arithmetic hypernym Collection.
• Second-order_arithmetic type Book.
• Second-order_arithmetic type Theory.
• Second-order_arithmetic comment "In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. It was introduced by David Hilbert and Paul Bernays in their book Grundlagen der Mathematik.".
• Second-order_arithmetic label "Second-order arithmetic".
• Second-order_arithmetic sameAs Q7442973.
• Second-order_arithmetic sameAs Aritmética_de_segundo_orden.
• Second-order_arithmetic sameAs Aritmética_de_segunda_ordem.
• Second-order_arithmetic sameAs m.09kh4g.
• Second-order_arithmetic sameAs Q7442973.
• Second-order_arithmetic wasDerivedFrom Second-order_arithmetic?oldid=707783065.
• Second-order_arithmetic isPrimaryTopicOf Second-order_arithmetic.