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Recursion Theory by Liang Yu, Chi Tat Chong

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6.5 Axiom of determinacy

In this book our focus is mostly on low level definable sets of reals such as those that are image or image. To go “higher up”, one resorts to the use of games and strategies which lie at the heart of the Axiom of Determinacy. It turns out that this axiom is at its core a large cardinal axiom.

6.5.1 Games and strategies

Let Aωω. An infinite game GA with perfect information has two players labeled I and II. The game is played by choosing a natural number alternately between the two players and ends in ω-many steps. Each game generates ...

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