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.
Andrzej Roslanowski
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