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.
@article{bwmeta1.element.doi-10_2478_s11533-010-0018-3,
author = {Saharon Shelah},
title = {Large continuum, oracles},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {213-234},
zbl = {1221.03051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0018-3}
}
Saharon Shelah. Large continuum, oracles. Open Mathematics, Tome 8 (2010) pp. 213-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0018-3/
[1] Shelah S., Properness without element aricity, Journal of Applied Analysis, 2004, 10, 168–289
[2] Shelah S., Non-cohenoracle c. c. c., Journal of Applied Analysis, 2006, 12, 1–17 http://dx.doi.org/10.1515/JAA.2006.1
[3] Shelah S., Acomment on “p < t”, Canadian Mathematical Bulletin, 2009, 52, 303–314 http://dx.doi.org/10.4153/CMB-2009-033-4