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- Large_cardinal abstract "In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least α such that α=ωα). The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC, and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott's phrase, as quantifying the fact "that if you want more you have to assume more".There is a rough convention that results provable from ZFC alone may be stated without hypotheses, but that if the proof requires other assumptions (such as the existence of large cardinals), these should be stated. Whether this is simply a linguistic convention, or something more, is a controversial point among distinct philosophical schools (see Motivations and epistemic status below).A large cardinal axiom is an axiom stating that there exists a cardinal (or perhaps many of them) with some specified large cardinal property.Most working set theorists believe that the large cardinal axioms that are currently being considered are consistent with ZFC. These axioms are strong enough to imply the consistency of ZFC. This has the consequence (via Gödel's second incompleteness theorem) that their consistency with ZFC cannot be proven in ZFC (assuming ZFC is consistent).There is no generally agreed precise definition of what a large cardinal property is, though essentially everyone agrees that those in the List of large cardinal properties are large cardinal properties.".
- Large_cardinal wikiPageExternalLink e.pdf.
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- Large_cardinal wikiPageRevisionID "671126451".
- Large_cardinal wikiPageWikiLink Akihiro_Kanamori.
- Large_cardinal wikiPageWikiLink Axiom_of_constructibility.
- Large_cardinal wikiPageWikiLink Axiomatic_system.
- Large_cardinal wikiPageWikiLink Axiomatization.
- Large_cardinal wikiPageWikiLink Cabal_(set_theory).
- Large_cardinal wikiPageWikiLink Cardinal_number.
- Large_cardinal wikiPageWikiLink Category:Large_cardinals.
- Large_cardinal wikiPageWikiLink Consistency.
- Large_cardinal wikiPageWikiLink Consistency_strength.
- Large_cardinal wikiPageWikiLink Consistent.
- Large_cardinal wikiPageWikiLink Constructible_universe.
- Large_cardinal wikiPageWikiLink Dana_Scott.
- Large_cardinal wikiPageWikiLink Equiconsistency.
- Large_cardinal wikiPageWikiLink Gxc3xb6dels_constructible_universe.
- Large_cardinal wikiPageWikiLink Gxc3xb6dels_incompleteness_theorem.
- Large_cardinal wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Large_cardinal wikiPageWikiLink Gxc3xb6dels_second_incompleteness_theorem.
- Large_cardinal wikiPageWikiLink Huge_cardinal.
- Large_cardinal wikiPageWikiLink Inaccessible_cardinal.
- Large_cardinal wikiPageWikiLink Linear_order.
- Large_cardinal wikiPageWikiLink List_of_large_cardinal_properties.
- Large_cardinal wikiPageWikiLink Martins_axiom.
- Large_cardinal wikiPageWikiLink Measurable_cardinal.
- Large_cardinal wikiPageWikiLink Ontological_maximalism.
- Large_cardinal wikiPageWikiLink Philosophy_of_mathematics.
- Large_cardinal wikiPageWikiLink Power_set.
- Large_cardinal wikiPageWikiLink Powerset.
- Large_cardinal wikiPageWikiLink Saharon_Shelah.
- Large_cardinal wikiPageWikiLink Set_theory.
- Large_cardinal wikiPageWikiLink Subset.
- Large_cardinal wikiPageWikiLink Supercompact_cardinal.
- Large_cardinal wikiPageWikiLink Total_order.
- Large_cardinal wikiPageWikiLink Transfinite_induction.
- Large_cardinal wikiPageWikiLink Transfinite_number.
- Large_cardinal wikiPageWikiLink Transitive_set.
- Large_cardinal wikiPageWikiLink Universe_(mathematics).
- Large_cardinal wikiPageWikiLink V=L.
- Large_cardinal wikiPageWikiLink Von_Neumann_universe.
- Large_cardinal wikiPageWikiLink W._Hugh_Woodin.
- Large_cardinal wikiPageWikiLink ZFC.
- Large_cardinal wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Large_cardinal wikiPageWikiLink Ω-conjecture.
- Large_cardinal wikiPageWikiLink Ω-logic.
- Large_cardinal wikiPageWikiLinkText "Large cardinal".
- Large_cardinal wikiPageWikiLinkText "large cardinal".
- Large_cardinal wikiPageWikiLinkText "large".
- Large_cardinal hasPhotoCollection Large_cardinal.
- Large_cardinal wikiPageUsesTemplate Template:Citation.
- Large_cardinal wikiPageUsesTemplate Template:Cite_arXiv.
- Large_cardinal wikiPageUsesTemplate Template:Cite_book.
- Large_cardinal wikiPageUsesTemplate Template:Cite_journal.
- Large_cardinal wikiPageUsesTemplate Template:Set_theory.
- Large_cardinal subject Category:Large_cardinals.
- Large_cardinal hypernym Kind.
- Large_cardinal comment "In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least α such that α=ωα).".
- Large_cardinal label "Large cardinal".
- Large_cardinal sameAs Velké_kardinály.
- Large_cardinal sameAs Große_Kardinalzahl.
- Large_cardinal sameAs Cardinal_grande.
- Large_cardinal sameAs Grand_cardinal.
- Large_cardinal sameAs מונה_גדול.
- Large_cardinal sameAs 巨大基数.
- Large_cardinal sameAs 큰_기수.
- Large_cardinal sameAs Groot_kardinaalgetal.
- Large_cardinal sameAs Duże_liczby_kardynalne.
- Large_cardinal sameAs Propriedade_de_grande_cardinal.
- Large_cardinal sameAs m.021y1f.
- Large_cardinal sameAs Stora_kardinaltal.
- Large_cardinal sameAs Великі_кардинальні_числа.
- Large_cardinal sameAs Q1548262.
- Large_cardinal sameAs Q1548262.
- Large_cardinal sameAs 大基数.
- Large_cardinal wasDerivedFrom Large_cardinal?oldid=671126451.
- Large_cardinal isPrimaryTopicOf Large_cardinal.