Cardinalities of noncentered systems of subsets of ω

✍ Scribed by Peter Vojtáš

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 340 KB
• Volume: 108
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90666-4

✦ Synopsis

VojtaS, P., Cardinalities of noncentered systems of subsets of w, Discrete Mathematics 108 (1992) 125-129.

We introduce a couple of new cardinal characteristics of o* which are equal to the minimal size of a system of infinite subsets of w satisfying some properties which were till now considered as a quality of ultrafilters, p-points and rapid filters respectively.

From this systems we do not require centeredness and hence they always exist. We give some estimations and equivalent reformulations and state problems concerning these new cardinal characteristics.

We say that a family 9 E [w] w is refining if for every X E [w]O there is an R~%suchthateitherR~*XorR~*o-X.

We say that a family V E C" is chaotic in T if for every X E [o]~ there is a c E Ce such that lim{c(n): n E X} does not exist.

We say that a family LG~ E [o]O is attractive for +? if for every c E T there is an X E d such that lim{c(n): n E X} does exist. We denote the corresponding