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Lecture(講演者): Carlos diPrisco
Title(タイトル): Parametrized Partition Relations
Level: Research lecture
形式(format): QuickTime(日本語) , QuickTime(English) (Version 7 or later)
Abstract(内容): We consider partitions relations defined on finite or infinite products of the Baire space. A set A of infinite sets of natural numbers is Ramsey if there is an infinite set X such that all of its infinite subsets are in A or none of them is in A, in this case we say that X is homogeneous for A. In Solovay's model all sets of reals (reals seen as infinite sets of integers) are Ramsey. Moreover, if for each x in the Cantor space we have a set of reals Ax, there is a perfect subset P of the Cantor space and an infinite set X of natural numbers such that X is homogeneous for all Ax with x in P. Stronger parametrized partition relations also hold in Solovay's model.
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Keywords: serial=0048, type=research lecture
License(ライセンス): No modification and free distribution. (creative commons, Attribution-NoDerivative works 2.1) Details

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