Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Axiom_of_projective_determinacy> ?p ?o }
Showing triples 1 to 45 of
45
with 100 triples per page.
- Axiom_of_projective_determinacy abstract "In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets.The axiom of projective determinacy, abbreviated PD, states that for any two-player game of perfect information of length ω in which the players play natural numbers, if the victory set (for either player, since the projective sets are closed under complementation) is projective, then one player or the other has a winning strategy.The axiom is not a theorem of ZFC (assuming ZFC is consistent), but unlike the full axiom of determinacy (AD), which contradicts the axiom of choice, it is not known to be inconsistent with ZFC. PD follows from certain large cardinal axioms, such as the existence of infinitely many Woodin cardinals.PD implies that all projective sets are Lebesgue measurable (in fact, universally measurable) and have the perfect set property and the property of Baire. It also implies that every projective binary relation may be uniformized by a projective set.".
- Axiom_of_projective_determinacy wikiPageID "1236592".
- Axiom_of_projective_determinacy wikiPageLength "1687".
- Axiom_of_projective_determinacy wikiPageOutDegree "18".
- Axiom_of_projective_determinacy wikiPageRevisionID "606665075".
- Axiom_of_projective_determinacy wikiPageWikiLink Axiom_of_choice.
- Axiom_of_projective_determinacy wikiPageWikiLink Axiom_of_determinacy.
- Axiom_of_projective_determinacy wikiPageWikiLink Binary_relation.
- Axiom_of_projective_determinacy wikiPageWikiLink Category:Descriptive_set_theory.
- Axiom_of_projective_determinacy wikiPageWikiLink Category:Determinacy.
- Axiom_of_projective_determinacy wikiPageWikiLink Category:Game_theory.
- Axiom_of_projective_determinacy wikiPageWikiLink Determinacy.
- Axiom_of_projective_determinacy wikiPageWikiLink Large_cardinal.
- Axiom_of_projective_determinacy wikiPageWikiLink Lebesgue_measurable.
- Axiom_of_projective_determinacy wikiPageWikiLink Lebesgue_measure.
- Axiom_of_projective_determinacy wikiPageWikiLink Mathematical_logic.
- Axiom_of_projective_determinacy wikiPageWikiLink Natural_number.
- Axiom_of_projective_determinacy wikiPageWikiLink Perfect_set_property.
- Axiom_of_projective_determinacy wikiPageWikiLink Projective_hierarchy.
- Axiom_of_projective_determinacy wikiPageWikiLink Projective_set.
- Axiom_of_projective_determinacy wikiPageWikiLink Property_of_Baire.
- Axiom_of_projective_determinacy wikiPageWikiLink Uniformization_(set_theory).
- Axiom_of_projective_determinacy wikiPageWikiLink Universally_measurable.
- Axiom_of_projective_determinacy wikiPageWikiLink Universally_measurable_set.
- Axiom_of_projective_determinacy wikiPageWikiLink Woodin_cardinal.
- Axiom_of_projective_determinacy wikiPageWikiLink ZFC.
- Axiom_of_projective_determinacy wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Axiom_of_projective_determinacy wikiPageWikiLinkText "Axiom of projective determinacy".
- Axiom_of_projective_determinacy wikiPageWikiLinkText "axiom of projective determinacy".
- Axiom_of_projective_determinacy hasPhotoCollection Axiom_of_projective_determinacy.
- Axiom_of_projective_determinacy wikiPageUsesTemplate Template:Cite_book.
- Axiom_of_projective_determinacy wikiPageUsesTemplate Template:Cite_journal.
- Axiom_of_projective_determinacy wikiPageUsesTemplate Template:Settheory-stub.
- Axiom_of_projective_determinacy subject Category:Descriptive_set_theory.
- Axiom_of_projective_determinacy subject Category:Determinacy.
- Axiom_of_projective_determinacy subject Category:Game_theory.
- Axiom_of_projective_determinacy hypernym Case.
- Axiom_of_projective_determinacy type Person.
- Axiom_of_projective_determinacy comment "In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets.The axiom of projective determinacy, abbreviated PD, states that for any two-player game of perfect information of length ω in which the players play natural numbers, if the victory set (for either player, since the projective sets are closed under complementation) is projective, then one player or the other has a winning strategy.The axiom is not a theorem of ZFC (assuming ZFC is consistent), but unlike the full axiom of determinacy (AD), which contradicts the axiom of choice, it is not known to be inconsistent with ZFC. ".
- Axiom_of_projective_determinacy label "Axiom of projective determinacy".
- Axiom_of_projective_determinacy sameAs m.04l044.
- Axiom_of_projective_determinacy sameAs Q4830557.
- Axiom_of_projective_determinacy sameAs Q4830557.
- Axiom_of_projective_determinacy wasDerivedFrom Axiom_of_projective_determinacy?oldid=606665075.
- Axiom_of_projective_determinacy isPrimaryTopicOf Axiom_of_projective_determinacy.