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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.".
- Implementation_of_mathematics_in_set_theory wikiPageExternalLink head.pdf.
- Implementation_of_mathematics_in_set_theory wikiPageExternalLink nf.html.
- Implementation_of_mathematics_in_set_theory wikiPageExternalLink quine-nf.
- Implementation_of_mathematics_in_set_theory wikiPageExternalLink settheory-alternative.
- Implementation_of_mathematics_in_set_theory wikiPageExternalLink us.metamath.org.
- Implementation_of_mathematics_in_set_theory wikiPageID "3486002".
- Implementation_of_mathematics_in_set_theory wikiPageRevisionID "602761065".
- Implementation_of_mathematics_in_set_theory hasPhotoCollection Implementation_of_mathematics_in_set_theory.
- 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.
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- 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 sameAs Q17101506.
- Implementation_of_mathematics_in_set_theory sameAs Q17101506.
- Implementation_of_mathematics_in_set_theory sameAs Implementation_of_mathematics_in_set_theory.
- Implementation_of_mathematics_in_set_theory wasDerivedFrom Implementation_of_mathematics_in_set_theory?oldid=602761065.
- Implementation_of_mathematics_in_set_theory isPrimaryTopicOf Implementation_of_mathematics_in_set_theory.