On Shelah's amalgamation
Haim Judah and Andrzej Roslanowski
We present a detailed explanation of three models of Shelah. We show the
role of the amalgamation in the construction of models in which all definable
sets of reals have Baire property or are Lebesgue measurable. Next we construct
a model in which every projective set of reals has Baire property, a model
with the Uniformization Property and a model of ZF + DC in
which all subsets of the real line are Lebesgue measurable but there is
a set without Baire property.
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