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II Workshop on Coverings, Selections and Games in Topology
December 19-22, 2005
University of Lecce
Lecce, Italy

Organizers
(Organizing Committee) Cosimo Guido, Anna Frascella, Domenico Lenzi, Gabriella Zammillo. (Scientific Committee) Liljana Babinkostova, Cosimo Guido, Ljubisa Kocinac, Marion Scheepers, Boaz Tsaban

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Borel planar sets without perfect rectangles
by
Wieslaw Kubis
Institute of Mathematics, Swietokrzyska Academy, Kielce, Poland

I shall describe a rank function on a given Borel planar set A, which "measures" the possibility of embeddability a perfect rectangle (i.e. a perfect set times a perfect set) into A. In fact, the rank depends on the tree representation of A. The rank of A is countable if and only if A does not contain a perfect rectangle. It turns out that, in the class of Fs planar sets, for each countable ordinal g there exists a universal Fs planar set of rank g. Such a set is unique (up to a certain kind of isomorphism). The universal set consistently contains rectangles of "large" cardinality (but no perfect ones).

Date received: November 30, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqh-31.