Pcf theory and cardinal invariants of the reals
Logic
2010-06-10 v1
Abstract
The additivity spectrum ADD(I) of an ideal I is the set of all regular cardinals kappa such that there is an increasing chain {A_alpha:alpha<kappa\} in the ideal I such that the union of the chain is not in I. We investigate which set A of regular cardinals can be the additivity spectrum of certain ideals. Assume that I=B or I=N, where B denotes the sigma-ideal generated by the compact subsets of the Baire space omega^omega, and N is the ideal of the null sets. For countable sets we give a full characterization of the additivity spectrum of I: a non-empty countable set A of uncountable regular cardinals can be ADD(I) in some c.c.c generic extension iff A=pcf(A).
Cite
@article{arxiv.1006.1808,
title = {Pcf theory and cardinal invariants of the reals},
author = {Lajos Soukup},
journal= {arXiv preprint arXiv:1006.1808},
year = {2010}
}
Comments
9 pages