15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 4 - Mathematische Logik, Theoretische Informatik
Donnerstag, 20. September 2001, 15.30, Hörsaal 46


Some implications in infinite combinatorics

Heike Mildenberger, Universität Wien


A cardinal characteristic is a cardinal number that describes a combinatorial or analytical property of the continuum. Like the power of the continuum itself, the size of a cardinal characteristic is often independent from ZFC. However, some restrictions on possible sizes follow from ZFC. In the talk, I shall show some of these restrictions for some well-known cardinal characteristics: $ \mathfrak{b}$ is the least size of an unbounded set in the order of eventual dominance on the set of functions from $ \omega$ to $ \omega$, and $ \mathfrak{g}$ is the groupwise density number, whose definition we shall recall in our talk.

[1] Andreas Blass: Groupwise density and related cardinals. Arch. Math. Logic 30 (1990), 1-11.
[2] Andreas Blass and Heike Mildenberger: On the cofinality of ultrapowers, Journal of Symbolic Logic 64 (1999), 727-736
[3] Heike Mildenberger: Groupwise dense families. Archive for Math. Logic 40 (2000), 93 -112.

E-Mail: heike@logic.univie.ac.at
Homepage: www.math.uni-bonn.de/people/heike

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