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- Axiom_of_determinacy abstract "In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω. AD states that every game of a certain type is determined; that is, one of the two players has a winning strategy.The axiom of determinacy is inconsistent with the axiom of choice (AC); the axiom of determinacy implies that all subsets of the real numbers are Lebesgue measurable, have the property of Baire, and the perfect set property. The last implies a weak form of the continuum hypothesis (namely, that every uncountable set of reals has the same cardinality as the full set of reals).Furthermore, AD implies the consistency of Zermelo–Fraenkel set theory (ZF). Hence, as a consequence of the incompleteness theorems, it is not possible to prove the relative consistency of ZF + AD with respect to ZF. It also implies the negation of the generalized continuum hypothesis, since GCH implies this axiom of choice, incompatible with AD (see below).".
- Axiom_of_determinacy wikiPageExternalLink 1987-RMJM-Telgarsky-Topological-Games.pdf.
- Axiom_of_determinacy wikiPageID "1002300".
- Axiom_of_determinacy wikiPageLength "10077".
- Axiom_of_determinacy wikiPageOutDegree "58".
- Axiom_of_determinacy wikiPageRevisionID "697716895".
- Axiom_of_determinacy wikiPageWikiLink AD+.
- Axiom_of_determinacy wikiPageWikiLink Axiom.
- Axiom_of_determinacy wikiPageWikiLink Axiom_of_choice.
- Axiom_of_determinacy wikiPageWikiLink Axiom_of_determinacy.
- Axiom_of_determinacy wikiPageWikiLink Axiom_of_projective_determinacy.
- Axiom_of_determinacy wikiPageWikiLink Axiom_of_real_determinacy.
- Axiom_of_determinacy wikiPageWikiLink Baire_space_(set_theory).
- Axiom_of_determinacy wikiPageWikiLink Banach–Mazur_game.
- Axiom_of_determinacy wikiPageWikiLink Borel_set.
- Axiom_of_determinacy wikiPageWikiLink Cardinality.
- Axiom_of_determinacy wikiPageWikiLink Cardinality_of_the_continuum.
- Axiom_of_determinacy wikiPageWikiLink Category:Axioms_of_set_theory.
- Axiom_of_determinacy wikiPageWikiLink Category:Determinacy.
- Axiom_of_determinacy wikiPageWikiLink Category:Large_cardinals.
- Axiom_of_determinacy wikiPageWikiLink Clopen_set.
- Axiom_of_determinacy wikiPageWikiLink Closed_set.
- Axiom_of_determinacy wikiPageWikiLink Consistency.
- Axiom_of_determinacy wikiPageWikiLink Continuum_hypothesis.
- Axiom_of_determinacy wikiPageWikiLink Countable_set.
- Axiom_of_determinacy wikiPageWikiLink Determinacy.
- Axiom_of_determinacy wikiPageWikiLink Donald_A._Martin.
- Axiom_of_determinacy wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Axiom_of_determinacy wikiPageWikiLink Hugo_Steinhaus.
- Axiom_of_determinacy wikiPageWikiLink Inaccessible_cardinal.
- Axiom_of_determinacy wikiPageWikiLink Infinitary_logic.
- Axiom_of_determinacy wikiPageWikiLink Jan_Mycielski.
- Axiom_of_determinacy wikiPageWikiLink Journal_of_the_American_Mathematical_Society.
- Axiom_of_determinacy wikiPageWikiLink L(R).
- Axiom_of_determinacy wikiPageWikiLink Large_cardinal.
- Axiom_of_determinacy wikiPageWikiLink Lebesgue_measure.
- Axiom_of_determinacy wikiPageWikiLink Martin_measure.
- Axiom_of_determinacy wikiPageWikiLink Measurable_cardinal.
- Axiom_of_determinacy wikiPageWikiLink Ordinal_number.
- Axiom_of_determinacy wikiPageWikiLink Perfect_set_property.
- Axiom_of_determinacy wikiPageWikiLink Proceedings_of_the_National_Academy_of_Sciences_of_the_United_States_of_America.
- Axiom_of_determinacy wikiPageWikiLink Projective_hierarchy.
- Axiom_of_determinacy wikiPageWikiLink Property_of_Baire.
- Axiom_of_determinacy wikiPageWikiLink Quantifier_(logic).
- Axiom_of_determinacy wikiPageWikiLink Rastislav_J._Telgársky.
- Axiom_of_determinacy wikiPageWikiLink Real_line.
- Axiom_of_determinacy wikiPageWikiLink Real_number.
- Axiom_of_determinacy wikiPageWikiLink Set_theory.
- Axiom_of_determinacy wikiPageWikiLink Topological_game.
- Axiom_of_determinacy wikiPageWikiLink Transfinite_induction.
- Axiom_of_determinacy wikiPageWikiLink W._Hugh_Woodin.
- Axiom_of_determinacy wikiPageWikiLink Well-order.
- Axiom_of_determinacy wikiPageWikiLink Woodin_cardinal.
- Axiom_of_determinacy wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Axiom_of_determinacy wikiPageWikiLinkText "AD".
- Axiom_of_determinacy wikiPageWikiLinkText "Axiom of determinacy".
- Axiom_of_determinacy wikiPageWikiLinkText "axiom of determinacy".
- Axiom_of_determinacy wikiPageWikiLinkText "certain type".
- Axiom_of_determinacy wikiPageWikiLinkText "determinacy".
- Axiom_of_determinacy wikiPageWikiLinkText "determined".
- Axiom_of_determinacy wikiPageUsesTemplate Template:Cite_book.
- Axiom_of_determinacy wikiPageUsesTemplate Template:Cite_journal.
- Axiom_of_determinacy subject Category:Axioms_of_set_theory.
- Axiom_of_determinacy subject Category:Determinacy.
- Axiom_of_determinacy subject Category:Large_cardinals.
- Axiom_of_determinacy hypernym Axiom.
- Axiom_of_determinacy comment "In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω.".
- Axiom_of_determinacy label "Axiom of determinacy".
- Axiom_of_determinacy sameAs Q4830558.
- Axiom_of_determinacy sameAs Determiniertheitsaxiom.
- Axiom_of_determinacy sameAs 決定性公理.
- Axiom_of_determinacy sameAs 결정_공리.
- Axiom_of_determinacy sameAs Aksjomat_determinacji.
- Axiom_of_determinacy sameAs m.03y8rm.
- Axiom_of_determinacy sameAs Q4830558.
- Axiom_of_determinacy wasDerivedFrom Axiom_of_determinacy?oldid=697716895.
- Axiom_of_determinacy isPrimaryTopicOf Axiom_of_determinacy.