Theorem

Borel Determinacy Theorem

Logic and Foundations

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 has a winning strategy for the game. A Gale-Stewart game is a possibly infinite two-player game in which both players have perfect information and no randomness is involved. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts

Classification

Statement Form

Existence Theorem 1

Proof Year

1975 1

Connections

Has Statement Form

Existence Theorem

In Branch

Set Theory

Source Borel determinacy theorem (Wikipedia)

Proved By

Donald A. Martin

Source Borel determinacy theorem (Wikipedia)

Sources

1. Borel determinacy theorem (Wikipedia)

Lead section
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.
Lead
It was proved by Donald A. Martin in 1975, and is applied in descriptive set theory to show that Borel sets in Polish spaces have regularity properties such as the perfect set property.
In Branch: Set Theory, Lead sentence
In descriptive set theory, the Borel determinacy theorem states that any Gale-Stewart game whose payoff set is a Borel set is dete
Proved By: Donald A. Martin, Lead sentence, attribution
proved by Donald A. Martin in 1975

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Borel Determinacy Theorem

Has Statement Form

In Branch

Proved By