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Borel Determinacy: A Streamlined Proof

Thomas Buffard, Gabriel Levrel, Sam Mayo

Abstract

First proved my Donald Martin in 1975, the result of Borel determinacy has been the subject of multiple revised proofs. Following Martin's book [1], we present a recent streamlined proof which implements ideas of Martin, Moschovakis, and Hurkens. We aim to give a concise presentation that makes this proof approachable to a wider audience.

Borel Determinacy: A Streamlined Proof

Abstract

First proved my Donald Martin in 1975, the result of Borel determinacy has been the subject of multiple revised proofs. Following Martin's book [1], we present a recent streamlined proof which implements ideas of Martin, Moschovakis, and Hurkens. We aim to give a concise presentation that makes this proof approachable to a wider audience.
Paper Structure (1 section, 7 theorems, 7 equations)

This paper contains 1 section, 7 theorems, 7 equations.

Table of Contents

  1. Acknowledgements.

Key Result

Lemma 1

The determinacy of games with taboos is level-by-level (of the Borel hierarchy) equivalent to the determinacy of infinite games without taboos (i.e. where the game tree is pruned).

Theorems & Definitions (18)

  • Definition
  • Definition
  • Definition
  • Lemma 1
  • proof
  • Definition
  • Lemma 2
  • proof
  • Corollary 3
  • proof
  • ...and 8 more