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| {{Noref|date=May 2011}}
| | I would like to introduce myself to you, I am Andrew and my spouse doesn't like it at all. The favorite hobby for him and his kids is to perform lacross and he would never give it up. For many years she's been working as a journey agent. For a whilst I've been in Alaska but I will have to move in a yr or two.<br><br>Here is my homepage :: online psychic ([http://www.seekavideo.com/playlist/2199/video/ http://www.seekavideo.com]) |
| In [[set theory]], the '''difference hierarchy''' over a [[pointclass]] is a [[hierarchy (mathematics)|hierarchy]] of larger pointclasses
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| generated by taking [[complement (set theory)|difference]]s of sets. If Γ is a pointclass, then the set of differences in Γ is <math>\{A:\exists C,D\in\Gamma ( A = C\setminus D)\}</math>. In usual notation, this set is denoted by 2-Γ. The next level of the hierarchy is denoted by 3-Γ and consists of differences of three sets:
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| <math>\{A : \exists C,D,E\in\Gamma ( A=C\setminus(D\setminus E))\}</math>. This definition can be extended recursively into the transfinite to α-Γ for some [[ordinal number|ordinal]] α.
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| In the [[Borel sets|Borel]] and [[projective set|projective hierarchies]], [[Felix Hausdorff]] proved that the countable levels of the
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| difference hierarchy over Π<sup>0</sup><sub style="margin-left:-0.6em">γ</sub> and Π<sup>1</sup><sub style="margin-left:-0.6em">γ</sub> give
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| Δ<sup>0</sup><sub style="margin-left:-0.6em">γ+1</sub> and Δ<sup>1</sup><sub style="margin-left:-0.6em">γ+1</sub>, respectively.
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| {{settheory-stub}}
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| [[Category:Descriptive set theory]]
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| [[Category:Mathematical logic hierarchies]]
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Latest revision as of 09:25, 27 November 2014
I would like to introduce myself to you, I am Andrew and my spouse doesn't like it at all. The favorite hobby for him and his kids is to perform lacross and he would never give it up. For many years she's been working as a journey agent. For a whilst I've been in Alaska but I will have to move in a yr or two.
Here is my homepage :: online psychic (http://www.seekavideo.com)