Kurt Gödel Research Center

2012 seminar talk: Relations between the I-ultrafilters

Talk held by Shuguo Zhang (Sichuan University, People's Republic of China) at the KGRC seminar on 2012-11-08.

Abstract

$I$-ultrafilters were introduced by J. Baumgartner in 1995. In this talk, under the continuum hypothesis, we show the following results:

• (1) There is a discrete ultrafilter which is not a $Z_0$-ultrafilter.
• (2) There is a $\sigma$-compact ultrafilter which is not a $Z_0$-ultrafilter.
• (3) There is a $J_3^\omega$ ultrafilter which is not a $Z_0$-ultrafilter, where $Z_0$ is the ideal of subsets of $\omega$ with asymptotic density zero.

This is joint work with Jianyong Hong.

Please note: This announcement brings a change of program. Martin Goldstern will give his talk in the research seminar on a later day.