Almost disjoint families and ultrapowers

Michalis Anoussis, Vaggelis Felouzis, Konstantinos Tsaprounis


We prove estimates for the cardinality of set-theoretic ultrapowers in terms of the cardinality of almost disjoint families. Such results are then applied to obtain estimates for the density of ultrapowers of Banach spaces. We focus on the change of the behavior of the corresponding ultrapower when certain ‘‘completeness thresholds’’ of the relevant ultrafilter are crossed. Finally, we also provide an alternative characterization of measurable cardinals.


Ultrafilters, Ultrapowers, Almost disjoint families, Banach spaces, epsilon-separated sets, Measurable cardinals

Full Text:

4. [PDF]


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Logic and Analysis ISSN:  1759-9008