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- Borel_determinacy_theorem abstract "In descriptive set theory, the Borel determinacy theorem states that any Gale-Stewart game whose winning 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.".
- Borel_determinacy_theorem wikiPageExternalLink thesis.pdf.
- Borel_determinacy_theorem wikiPageID "15483838".
- Borel_determinacy_theorem wikiPageRevisionID "537057795".
- Borel_determinacy_theorem hasPhotoCollection Borel_determinacy_theorem.
- Borel_determinacy_theorem subject Category:Determinacy.
- Borel_determinacy_theorem subject Category:Theorems_in_the_foundations_of_mathematics.
- Borel_determinacy_theorem type Abstraction100002137.
- Borel_determinacy_theorem type Communication100033020.
- Borel_determinacy_theorem type Message106598915.
- Borel_determinacy_theorem type Proposition106750804.
- Borel_determinacy_theorem type Statement106722453.
- Borel_determinacy_theorem type Theorem106752293.
- Borel_determinacy_theorem type TheoremsInTheFoundationsOfMathematics.
- Borel_determinacy_theorem comment "In descriptive set theory, the Borel determinacy theorem states that any Gale-Stewart game whose winning 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.".
- Borel_determinacy_theorem label "Borel determinacy theorem".
- Borel_determinacy_theorem sameAs m.03mbvft.
- Borel_determinacy_theorem sameAs Q4944906.
- Borel_determinacy_theorem sameAs Q4944906.
- Borel_determinacy_theorem sameAs Borel_determinacy_theorem.
- Borel_determinacy_theorem wasDerivedFrom Borel_determinacy_theorem?oldid=537057795.
- Borel_determinacy_theorem isPrimaryTopicOf Borel_determinacy_theorem.