2013 seminar talk: Van der Waerden ideal and its cardinal invariants

Talk held by Jana Flašková (University of West Bohemia in Pilsen, Czech Republic) at the KGRC seminar on 2013-01-17.


The sets which do not contain arbitrarily long arithmetic progressions form an ideal on the natural numbers, which is called van der Waerden ideal. The structure of the van der Waerden ideal and its relation to other well-known ideals on the natural numbers will be the subject of this talk. We shall also discuss some cardinal invariants of the ideal such as additivity, cofinality, uniformity and covering number. For example, we will show that the uniformity number of the van der Waerden ideal is less or equal to the reaping number.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.