English

Coherent Adequate Forcing and Preserving CH

Logic 2014-06-13 v1

Abstract

We develop a general framework for forcing with coherent adequate sets on H(λ)H(\lambda) as side conditions, where λω2\lambda \ge \omega_2 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 ω2\omega_2 with finite conditions while preserving CH, solving a problem of Friedman.

Keywords

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}
}
R2 v1 2026-06-22T04:37:22.420Z