Acoustic wave equation: Difference between revisions

Revision as of 06:12, 28 January 2014

In descriptive set theory, a lightface analytic game is a game whose payoff set A is a $Σ_{1}^{1}$ subset of Baire space; that is, there is a tree T on $ω \times ω$ which is a computable subset of $(ω \times ω)^{< ω}$ , 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^#.

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+In [[descriptive set theory]], a '''lightface analytic game''' is a [[Determinacy#Games|game]] whose [[Determinacy#Games|payoff set]] ''A'' is a <math>\Sigma^1_1</math> [[subset]] of [[Baire space (set theory)|Baire space]]; 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 [[Zero sharp|0<sup>#</sup>]].
+[[Category:Effective descriptive set theory]]
+[[Category:Determinacy]]
+{{mathlogic-stub}}