Large continuum, oracles

2007/07/12 by Shelah, Saharon
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.0707.1818

Abstract

Our main theorem is about iterated forcing for making the continuum larger than aleph₂. We present a generalization of math.LO/0303294 which is dealing with oracles for random, etc., replacing aleph₁, aleph₂ by lambda,lambda⁺ (starting with lambda=lambda^aleph₁). 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.

Related

• Long iterations for the continuum
• Countable support iterations and large continuum
• Corrected Iteration
• A generic absoluteness principle consistent with large continuum
• A more general iterable condition ensuring aleph₁ is not collapsed