Lightface analytic game: Difference between revisions

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In [[descriptive set theory]], a '''lightface analytic game''' is a [[Determinacy#Games|game]] whose payoff set ''A'' is a <math>\Sigma^1_1</math> subset of [[Baire space (set theory)]]; that is, there is a [[Tree (descriptive set theory)|tree]] ''T'' on <math>\omega\times\omega</math> which is a [[computable]] [[subset]] of <math>(\omega\times\omega)^{<\omega}</math>, such that ''A'' is the projection of the set of all branches of ''T''.

The [[determinacy]] of all ''lightface analytic games'' is equivalent to the existence of [[0#]].

[[Category:Descriptive set theory]]