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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 infinitesimal elements.".
- Internal_set_theory wikiPageExternalLink books.html.
- Internal_set_theory wikiPageID "865686".
- Internal_set_theory wikiPageRevisionID "577435834".
- Internal_set_theory hasPhotoCollection Internal_set_theory.
- Internal_set_theory subject Category:Non-standard_analysis.
- Internal_set_theory subject Category:Systems_of_set_theory.
- Internal_set_theory type Artifact100021939.
- Internal_set_theory type Instrumentality103575240.
- Internal_set_theory type Object100002684.
- Internal_set_theory type PhysicalEntity100001930.
- Internal_set_theory type System104377057.
- Internal_set_theory type SystemsOfSetTheory.
- Internal_set_theory type Whole100003553.
- 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 label "Interne Mengenlehre".
- Internal_set_theory sameAs Interne_Mengenlehre.
- Internal_set_theory sameAs m.03jrk1.
- Internal_set_theory sameAs Q1666284.
- Internal_set_theory sameAs Q1666284.
- Internal_set_theory sameAs Internal_set_theory.
- Internal_set_theory wasDerivedFrom Internal_set_theory?oldid=577435834.
- Internal_set_theory isPrimaryTopicOf Internal_set_theory.