Open AccessAlmost disjoint families and ultrapowers
Author(s) -
M. Anoussis,
V. Felouzis,
Konstantinos Tsaprounis
Publication year - 2021
Publication title -
journal of logic and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.278
H-Index - 4
ISSN - 1759-9008
DOI - 10.4115/jla.2021.13.4
Subject(s) - ultraproduct , disjoint sets , cardinality (data modeling) , mathematics , ultrafilter , cardinal number (linguistics) , completeness (order theory) , characterization (materials science) , regular cardinal , discrete mathematics , set (abstract data type) , combinatorics , computer science , data mining , mathematical analysis , linguistics , philosophy , materials science , programming language , nanotechnology
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.