  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.
