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

Connections

Has Statement Form

Existence Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Set Theory

Source Borel determinacy theorem (Wikipedia)

Sources

1. Borel determinacy theorem (Wikipedia)

In Branch: Set Theory, Lead sentence

Quote, 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

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Borel Determinacy Theorem

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In Branch