Central European Journal of Mathematics

, Volume 8, Issue 2, pp 213–234

Large continuum, oracles

Research Article

DOI: 10.2478/s11533-010-0018-3

Cite this article as:
Shelah, S. centr.eur.j.math. (2010) 8: 213. doi:10.2478/s11533-010-0018-3


Our main theorem is about iterated forcing for making the continuum larger than ℵ2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing ℵ1,ℵ2 by λ, λ+ (starting with λ = λ<λ > ℵ1). Well, we demand absolute c.c.c. So we get, e.g. the continuum is λ+ but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a “partial” countable support iteration but it is c.c.c.


Iterated forcingCountable chain conditionLarge continuumPeculiar cuts



Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2010

Authors and Affiliations

  1. 1.Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat RamThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of Mathematics, Hill Center — Busch CampusThe State University of New JerseyRutgersUSA