Violating the Singular Cardinals Hypothesis Without Large Cardinals
Logic
2011-07-11 v1
Abstract
We extend a transitive model V of ZFC + GCH cardinal preservingly to a model N of ZF + "GCH holds below Alef_omega" + "there is a surjection from the power set of Alef_omega onto lambda" where lambda is an arbitrarily high fixed cardinal in V.
Cite
@article{arxiv.1107.1667,
title = {Violating the Singular Cardinals Hypothesis Without Large Cardinals},
author = {Moti Gitik and Peter Koepke},
journal= {arXiv preprint arXiv:1107.1667},
year = {2011}
}
Comments
18 pages, to appear in Israel Journal of Mathematics