In the mathematical practice, the Baire category method is a tool
for establishing the existence of a rich array of generic
structures. However, in mathematics, the Baire category method is
also behind a number of fundamental results such as the Open
Mapping Theorem or the Banach-Steinhaus Boundedness Principle. This
volume brings the Baire category method to another level of
sophistication via the internal version of the set-theoretic
forcing technique. It is the first systematic account of
applications of the higher forcing axioms with the stress on the
technique of building forcing notions rather than on the
relationship between different forcing axioms or their consistency
strengths.
General
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