Coherent adequate forcing and preserving CH

John Krueger, Miguel Angel Mota
2015 Journal of Mathematical Logic  
We develop a general framework for forcing with coherent adequate sets on H(λ) as side conditions, where λ ≥ ω 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 ω 2 with finite conditions while preserving CH, solving a problem of Friedman [3].
doi:10.1142/s0219061315500051 fatcat:m3lvu6bfbferxiokyanazdt5ki