English

Countable support iterations and large continuum

Logic 2016-09-07 v1

Abstract

We prove that any countable support iteration formed with posets with ω2\omega_2-p.i.c.\ has ω2\omega_2-c.c., assuming CH in the ground model and assuming also that ω1\omega_1 is not collapsed. This improves earlier results of Shelah by removing the restriction on the length of the iteration. Thus, we solve the problem of obtaining a large continuum via such forcing iterations.

Keywords

Cite

@article{arxiv.math/9702204,
  title  = {Countable support iterations and large continuum},
  author = {Chaz Schlindwein},
  journal= {arXiv preprint arXiv:math/9702204},
  year   = {2016}
}