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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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Scales, fields, and a problem of Hurewicz
by
Boaz Tsaban
The Weizmann Institute of Science
Coauthors: Lubomyr Zdomsky

Menger's basis property is a generalization of s-compactness which admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non s-compact sets of reals with Menger's property. Special instances of these constructions give known counter-examples to conjectures of Menger and Hurewicz. We obtain the first constructive solution to the Hurewicz 1927 problem, which was recently raised again in several places by Bukovský and others.

The constructed sets generate nontrivial subfields of the real line with strong combinatorial properties, and most of our results can be stated in a Ramsey-theoretic manner.

Paper reference: arXiv:math.GN/0507043

Date received: September 4, 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-03.