Large continuum, oracles

by Shelah. [Sh:895]
Central European J Math, 2010
Our main theorem is about iterated forcing for making the continuum larger than aleph_2 . We present a generalization of [Sh:669] which is dealing with oracles for random, etc., replacing aleph_1, aleph_2 by lambda, lambda^+ (starting with lambda = lambda^{< lambda} > aleph_1). 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 also give some applications related to peculiar cuts of [Sh:885].

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