Coherent Adequate Forcing and Preserving CH
Logic
2014-06-13 v1
Abstract
We develop a general framework for forcing with coherent adequate sets on as side conditions, where is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of with finite conditions while preserving CH, solving a problem of Friedman.
Cite
@article{arxiv.1406.3302,
title = {Coherent Adequate Forcing and Preserving CH},
author = {John Krueger and Miguel Angel Mota},
journal= {arXiv preprint arXiv:1406.3302},
year = {2014}
}