Not collapsing cardinals <= kappa in (< kappa) --support iterations
Logic
2016-09-07 v1
Abstract
We deal with the problem of preserving various versions of completeness in (< kappa) --support iterations of forcing notions, generalizing the case ``S --complete proper is preserved by CS iterations for a stationary co-stationary S subseteq omega_1''. We give applications to Uniformization and the Whitehead problem. In particular, for a strongly inaccessible cardinal kappa and a stationary set S subseteq kappa with fat complement we can have uniformization for < A_delta : delta in S'>, A_delta subseteq delta = sup A_delta, cf(delta)=otp(A_delta) and a stationary non-reflecting set S' subseteq S .
Keywords
Cite
@article{arxiv.math/9707225,
title = {Not collapsing cardinals <= kappa in (< kappa) --support iterations},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9707225},
year = {2016}
}