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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

Forcing (Model theory) --- Axioms. --- Baire classes. --- Baire class --- Baire classification --- Baire's class --- Baire's classification --- Class, Baire --- Classes, Baire --- Classification, Baire --- Functions of real variables --- Geometry --- Mathematics --- Parallels (Geometry) --- Philosophy --- Model theory --- Foundations