Killing the GCH everywhere with a single real
Logic
2015-10-13 v1
Abstract
Shelah-Woodin investigate the possibility of violating instances of through the addition of a single real. In particular they show that it is possible to obtain a failure of by adding a single real to a model of , preserving cofinalities. In this article we strengthen their result by showing that it is possible to violate at all infinite cardinals by adding a single real to a model of Our assumption is the existence of an -strong cardinal, by work of Gitik and Mitchell it is known that more than an -strong cardinal is required.
Cite
@article{arxiv.1510.02933,
title = {Killing the GCH everywhere with a single real},
author = {Sy David Friedman and Mohammad Golshani},
journal= {arXiv preprint arXiv:1510.02933},
year = {2015}
}