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- Implementation_of_mathematics_in_set_theory abstract "This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine's New Foundations shown to be consistent by R. B. Jensen in 1969 (here understood to include at least axioms of Infinity and Choice).What is said here applies also to two families of set theories: on the one hand, a range of theories including Zermelo set theory near the lower end of the scale and going up to ZFC extended with large cardinal hypotheses such as \"there is a measurable cardinal\"; and on the other hand a hierarchy of extensions of NFU which is surveyed in the New Foundations article. These correspond to different general views of what the set-theoretical universe is like, and it is the approaches to implementation of mathematical concepts under these two general views that are being compared and contrasted.It is not the primary aim of this article to say anything about the relative merits of these theories as foundations for mathematics. The reason for the use of two different set theories is to illustrate that multiple approaches to the implementation of mathematics are feasible. Precisely because of this approach, this article is not a source of \"official\" definitions for any mathematical concept.".
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Antisymmetric_relation.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Axiom_of_choice.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Axiom_of_union.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Axiom_schema_of_replacement.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Category:Formalism_(deductive).
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Category:Large-scale_mathematical_formalization_projects.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Category:Mathematical_logic.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Category:Set_theory.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Class_(set_theory).
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Composition_of_relations.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Dana_Scott.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Image_(mathematics).
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Injective_function.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Keith_Devlin.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Large_cardinal.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Mahlo_cardinals.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Measurable_cardinal.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Mirimanoffs_paradox.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink New_Foundations.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Predicate_(mathematical_logic).
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Principia_Mathematica.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Projection_(mathematics).
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Reflexive_relation.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Schröder–Bernstein_theorem.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Stanford_Encyclopedia_of_Philosophy.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Transfinite_induction.
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- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Union_(set_theory).
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Up_to.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Urelement.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Von_Neumann_universe.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Von_Neumann–Bernays–Gödel_set_theory.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Well-founded_relation.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Well-order.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Zermelo_set_theory.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Implementation_of_mathematics_in_set_theory wikiPageWikiLinkText "Implementation of mathematics in set theory".
- Implementation_of_mathematics_in_set_theory wikiPageWikiLinkText "all objects are sets".
- Implementation_of_mathematics_in_set_theory wikiPageWikiLinkText "formalization of mathematics".
- Implementation_of_mathematics_in_set_theory wikiPageWikiLinkText "implementation of mathematics in set theory".
- Implementation_of_mathematics_in_set_theory wikiPageWikiLinkText "implemented".
- Implementation_of_mathematics_in_set_theory wikiPageUsesTemplate Template:Main.
- Implementation_of_mathematics_in_set_theory subject Category:Formalism_(deductive).
- Implementation_of_mathematics_in_set_theory subject Category:Large-scale_mathematical_formalization_projects.
- Implementation_of_mathematics_in_set_theory subject Category:Mathematical_logic.
- Implementation_of_mathematics_in_set_theory subject Category:Set_theory.
- Implementation_of_mathematics_in_set_theory type Field.
- Implementation_of_mathematics_in_set_theory type Theory.
- Implementation_of_mathematics_in_set_theory comment "This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine's New Foundations shown to be consistent by R. B.".
- Implementation_of_mathematics_in_set_theory label "Implementation of mathematics in set theory".
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- Implementation_of_mathematics_in_set_theory wasDerivedFrom Implementation_of_mathematics_in_set_theory?oldid=621877049.
- Implementation_of_mathematics_in_set_theory isPrimaryTopicOf Implementation_of_mathematics_in_set_theory.