Continuous images of big sets and additivity of
s0 under CPAprism
and Janusz Pawlikowski
Real Anal. Exchange 29(2) (2003--2004), 755-762.
We prove that the Covering Property Axiom CPAprism,
which holds in the iterated perfect set model, implies the following facts.
There exists a family G of uniformly continuous functions from R
to [0,1] such that G has cardinality \omega1 < \continuum and for every
subset S of R of cardinality
\continuum there exists a g in G with g[S]=[0,1].
The additivity of the Marczewski's ideal s0 is equal to \omega1 < \continuum.
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Last modified October 6, 2004.