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- Borel_determinacy_theorem abstract "In descriptive set theory, the Borel determinacy theorem states that any Gale-Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. It was proved by Donald A. Martin in 1975. The theorem is applied in descriptive set theory to show that Borel sets in Polish spaces have regularity properties such as the perfect set property and the property of Baire.The theorem is also known for its metamathematical properties. In 1971, before the theorem was proved, Harvey Friedman showed that any proof of the theorem in Zermelo-Fraenkel set theory must make repeated use of the axiom of replacement. Later results showed that stronger determinacy theorems cannot be proven in Zermelo-Fraenkel set theory, although they are relatively consistent with it if certain large cardinals are consistent.".
- Borel_determinacy_theorem wikiPageExternalLink thesis.pdf.
- Borel_determinacy_theorem wikiPageID "15483838".
- Borel_determinacy_theorem wikiPageLength "12008".
- Borel_determinacy_theorem wikiPageOutDegree "64".
- Borel_determinacy_theorem wikiPageRevisionID "677877419".
- Borel_determinacy_theorem wikiPageWikiLink Analytic_set.
- Borel_determinacy_theorem wikiPageWikiLink Annals_of_Mathematics.
- Borel_determinacy_theorem wikiPageWikiLink Axiom_of_choice.
- Borel_determinacy_theorem wikiPageWikiLink Axiom_of_dependent_choice.
- Borel_determinacy_theorem wikiPageWikiLink Axiom_of_determinacy.
- Borel_determinacy_theorem wikiPageWikiLink Axiom_of_projective_determinacy.
- Borel_determinacy_theorem wikiPageWikiLink Axiom_schema_of_replacement.
- Borel_determinacy_theorem wikiPageWikiLink Baire_space.
- Borel_determinacy_theorem wikiPageWikiLink Base_(topology).
- Borel_determinacy_theorem wikiPageWikiLink Borel_hierarchy.
- Borel_determinacy_theorem wikiPageWikiLink Borel_set.
- Borel_determinacy_theorem wikiPageWikiLink Cantor_space.
- Borel_determinacy_theorem wikiPageWikiLink Category:Determinacy.
- Borel_determinacy_theorem wikiPageWikiLink Category:Theorems_in_the_foundations_of_mathematics.
- Borel_determinacy_theorem wikiPageWikiLink Closed_set.
- Borel_determinacy_theorem wikiPageWikiLink Consistency.
- Borel_determinacy_theorem wikiPageWikiLink Countable_set.
- Borel_determinacy_theorem wikiPageWikiLink Cumulative_hierarchy.
- Borel_determinacy_theorem wikiPageWikiLink Descriptive_set_theory.
- Borel_determinacy_theorem wikiPageWikiLink Determinacy.
- Borel_determinacy_theorem wikiPageWikiLink Discrete_space.
- Borel_determinacy_theorem wikiPageWikiLink Donald_A._Martin.
- Borel_determinacy_theorem wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Borel_determinacy_theorem wikiPageWikiLink Harvey_Friedman.
- Borel_determinacy_theorem wikiPageWikiLink Inaccessible_cardinal.
- Borel_determinacy_theorem wikiPageWikiLink Large_cardinal.
- Borel_determinacy_theorem wikiPageWikiLink Mathematical_Reviews.
- Borel_determinacy_theorem wikiPageWikiLink Measurable_cardinal.
- Borel_determinacy_theorem wikiPageWikiLink Metamathematics.
- Borel_determinacy_theorem wikiPageWikiLink Open_set.
- Borel_determinacy_theorem wikiPageWikiLink Perfect_set_property.
- Borel_determinacy_theorem wikiPageWikiLink Polish_space.
- Borel_determinacy_theorem wikiPageWikiLink Power_set.
- Borel_determinacy_theorem wikiPageWikiLink Product_topology.
- Borel_determinacy_theorem wikiPageWikiLink Projective_hierarchy.
- Borel_determinacy_theorem wikiPageWikiLink Property_of_Baire.
- Borel_determinacy_theorem wikiPageWikiLink Sigma-algebra.
- Borel_determinacy_theorem wikiPageWikiLink Subset.
- Borel_determinacy_theorem wikiPageWikiLink Topology.
- Borel_determinacy_theorem wikiPageWikiLink Tree_(descriptive_set_theory).
- Borel_determinacy_theorem wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Borel_determinacy_theorem wikiPageWikiLinkText "Borel determinacy theorem".
- Borel_determinacy_theorem wikiPageUsesTemplate Template:Cite_book.
- Borel_determinacy_theorem wikiPageUsesTemplate Template:Cite_journal.
- Borel_determinacy_theorem wikiPageUsesTemplate Template:MR.
- Borel_determinacy_theorem wikiPageUsesTemplate Template:Main.
- Borel_determinacy_theorem subject Category:Determinacy.
- Borel_determinacy_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Borel_determinacy_theorem hypernym Borel.
- Borel_determinacy_theorem type Theorem.
- Borel_determinacy_theorem comment "In descriptive set theory, the Borel determinacy theorem states that any Gale-Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. It was proved by Donald A. Martin in 1975. The theorem is applied in descriptive set theory to show that Borel sets in Polish spaces have regularity properties such as the perfect set property and the property of Baire.The theorem is also known for its metamathematical properties.".
- Borel_determinacy_theorem label "Borel determinacy theorem".
- Borel_determinacy_theorem sameAs Q4944906.
- Borel_determinacy_theorem sameAs m.03mbvft.
- Borel_determinacy_theorem sameAs Q4944906.
- Borel_determinacy_theorem wasDerivedFrom Borel_determinacy_theorem?oldid=677877419.
- Borel_determinacy_theorem isPrimaryTopicOf Borel_determinacy_theorem.