On cardinalities in quotients of inverse limits of groups
Logic
2007-05-23 v1
Abstract
Let lambda be aleph_0 or a strong limit of cofinality aleph_0. Suppose that (G_m,p_{m,n}:m =< n<omega) and (H_m,p^t_{m,n}: m=< n < omega) are projective systems of groups of cardinality less than lambda and suppose that for every n<omega there is a homomorphism h:H_n-->G_n such that all the diagrams commute. If for every mu<lambda there exists (f_i in G_omega:i<mu) such that for distinct i,j we have: f_i f_j^{-1} notin h_omega(H_omega), then there exists (f_i in G_omega:i<2^lambda) such that for distinct i,j we have f_i f_j^{-1} notin h_omega(H_omega).
Keywords
Cite
@article{arxiv.math/9911225,
title = {On cardinalities in quotients of inverse limits of groups},
author = {Rami Grossberg and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9911225},
year = {2007}
}