English

Large continuum, oracles

Logic 2010-03-03 v2

Abstract

Our main theorem is about iterated forcing for making the continuum larger than aleph_2. We present a generalization of math.LO/0303294 which is dealing with oracles for random, etc., replacing aleph_1, aleph_2 by lambda,lambda^+ (starting with lambda=lambda^{<lambda}>aleph_1). Well, instead of properness we demand absolute c.c.c. So we get, e.g. the continuum is lambda^+ but we can get cov(meagre)=lambda. We give some applications. As in math.LO/0303294, it is a "partial" countable support iteration but it is c.c.c.

Keywords

Cite

@article{arxiv.0707.1818,
  title  = {Large continuum, oracles},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:0707.1818},
  year   = {2010}
}
R2 v1 2026-06-21T08:57:39.093Z