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...

game) determinacy for a boldface pointclass implies Blackwell determinacy for the pointclass. This, combined with the Borel determinacy theorem of Martin...

closed set, then the game is determined. By the Borel determinacy theorem, games whose winning set is a Borel set are determined. It follows from the existence...

theorem Heine–Borel theorem Borel determinacy theorem Borel right process Borel set Borel summation Borel distribution Borel's conjecture about strong measure...

Borel–Carathéodory theorem (complex analysis) Borel–Weil theorem (representation theory) Borel determinacy theorem (set theory) Borel fixed-point theorem (algebraic...

replacement are required to show that Borel games are determined. The proven result is Donald A. Martin's Borel determinacy theorem. A later, more careful analysis...

Lebesgue measure 0. If the axiom of determinacy holds then all sets of reals are Lebesgue-measurable. Determinacy is however not compatible with the axiom...

Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets...

that Brouwer's theorem is equivalent to the determinacy theorem for Hex. The Lefschetz fixed-point theorem says that if a continuous map f from a finite...

projective determinacy, all projective sets have both the perfect set property and the property of Baire. This is related to the fact that ZFC proves Borel determinacy...