Borel Families of Games

Alexander Kastner; Clark Lyons

Borel Families of Games

Alexander Kastner, Clark Lyons

Abstract

We give an elementary proof that in a Borel family of games, the set of games for which player II has a winning strategy is Baire measurable, universally measurable, and completely Ramsey in the case where $X = [\mathbb{N}]^{\aleph_0}$.

Borel Families of Games

Abstract

Paper Structure (7 theorems, 13 equations)

This paper contains 7 theorems, 13 equations.

Key Result

Theorem 1

Let $X$ be a Polish space, and suppose that $B \subseteq X \times \mathcal{N}$ is a Borel family of games. Then is Baire measurable and universally measurable. In the case where $X = [\mathbb{N}]^{\aleph_0}$, the set $W$ is also completely Ramsey.

Theorems & Definitions (13)

Theorem 1
Definition 2
Theorem 3
proof
Proposition 4
proof
Corollary 5
Theorem 6: General Borel Determinacy
Theorem 7
proof
...and 3 more