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- Internal_set_theory abstract "Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the non-standard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, Nelson's approach modifies the axiomatic foundations through syntactic enrichment. Thus, the axioms introduce a new term, "standard", which can be used to make discriminations not possible under the conventional axioms for sets. Thus, IST is an enrichment of ZFC: all axioms of ZFC are satisfied for all classical predicates, while the new unary predicate "standard" satisfies three additional axioms I, S, and T. In particular, suitable non-standard elements within the set of real numbers can be shown to have properties that correspond to the properties of infinitesimal and unlimited elements.Nelson's formulation is made more accessible for the lay-mathematician by leaving out many of the complexities of meta-mathematical logic that were initially required to justify rigorously the consistency of number systems containing infinitesimal elements.".
- Internal_set_theory wikiPageExternalLink books.html.
- Internal_set_theory wikiPageID "865686".
- Internal_set_theory wikiPageLength "14680".
- Internal_set_theory wikiPageOutDegree "33".
- Internal_set_theory wikiPageRevisionID "625657200".
- Internal_set_theory wikiPageWikiLink Abraham_Robinson.
- Internal_set_theory wikiPageWikiLink Augustin-Louis_Cauchy.
- Internal_set_theory wikiPageWikiLink Axiom_of_choice.
- Internal_set_theory wikiPageWikiLink Axiom_of_replacement.
- Internal_set_theory wikiPageWikiLink Axiom_of_separation.
- Internal_set_theory wikiPageWikiLink Axiom_schema_of_replacement.
- Internal_set_theory wikiPageWikiLink Axiom_schema_of_specification.
- Internal_set_theory wikiPageWikiLink Category:Non-standard_analysis.
- Internal_set_theory wikiPageWikiLink Category:Systems_of_set_theory.
- Internal_set_theory wikiPageWikiLink Conservative_extension.
- Internal_set_theory wikiPageWikiLink Consistency.
- Internal_set_theory wikiPageWikiLink Definable_number.
- Internal_set_theory wikiPageWikiLink Definable_real_number.
- Internal_set_theory wikiPageWikiLink Edward_Nelson.
- Internal_set_theory wikiPageWikiLink Finitism.
- Internal_set_theory wikiPageWikiLink First-order_logic.
- Internal_set_theory wikiPageWikiLink Georg_Cantor.
- Internal_set_theory wikiPageWikiLink Gottfried_Leibniz.
- Internal_set_theory wikiPageWikiLink Gottfried_Wilhelm_Leibniz.
- Internal_set_theory wikiPageWikiLink Great_circle.
- Internal_set_theory wikiPageWikiLink Infinitesimal.
- Internal_set_theory wikiPageWikiLink Johann_Bernoulli.
- Internal_set_theory wikiPageWikiLink Karel_Hrbacek.
- Internal_set_theory wikiPageWikiLink Karel_Hrbáček.
- Internal_set_theory wikiPageWikiLink Karl_Weierstrass.
- Internal_set_theory wikiPageWikiLink Leonhard_Euler.
- Internal_set_theory wikiPageWikiLink Logic.
- Internal_set_theory wikiPageWikiLink Logically_consistent.
- Internal_set_theory wikiPageWikiLink Model_theory.
- Internal_set_theory wikiPageWikiLink Non-Euclidean_geometry.
- Internal_set_theory wikiPageWikiLink Non-standard_analysis.
- Internal_set_theory wikiPageWikiLink Real_number.
- Internal_set_theory wikiPageWikiLink Richard_Dedekind.
- Internal_set_theory wikiPageWikiLink Set_(mathematics).
- Internal_set_theory wikiPageWikiLink Signature_(logic).
- Internal_set_theory wikiPageWikiLink Zermelo–Fraenkel_axioms.
- Internal_set_theory wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Internal_set_theory wikiPageWikiLinkText "Internal Set Theory".
- Internal_set_theory wikiPageWikiLinkText "Internal set theory".
- Internal_set_theory wikiPageWikiLinkText "internal set theory".
- Internal_set_theory hasPhotoCollection Internal_set_theory.
- Internal_set_theory wikiPageUsesTemplate Template:.
- Internal_set_theory wikiPageUsesTemplate Template:=.
- Internal_set_theory wikiPageUsesTemplate Template:Infinitesimals.
- Internal_set_theory wikiPageUsesTemplate Template:Reflist.
- Internal_set_theory subject Category:Non-standard_analysis.
- Internal_set_theory subject Category:Systems_of_set_theory.
- Internal_set_theory hypernym Theory.
- Internal_set_theory type Book.
- Internal_set_theory type Field.
- Internal_set_theory comment "Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the non-standard analysis introduced by Abraham Robinson. Instead of adding new elements to the real numbers, Nelson's approach modifies the axiomatic foundations through syntactic enrichment. Thus, the axioms introduce a new term, "standard", which can be used to make discriminations not possible under the conventional axioms for sets.".
- Internal_set_theory label "Internal set theory".
- Internal_set_theory sameAs Interne_Mengenlehre.
- Internal_set_theory sameAs m.03jrk1.
- Internal_set_theory sameAs Внутрішня_теорія_множин.
- Internal_set_theory sameAs Q1666284.
- Internal_set_theory sameAs Q1666284.
- Internal_set_theory wasDerivedFrom Internal_set_theory?oldid=625657200.
- Internal_set_theory isPrimaryTopicOf Internal_set_theory.