Notes On Forcing Axioms

Stevo Todorcevic

dhj 2013 · Lecture Notes Series, Institute For Mathematical Sciences, National University Of Singapore Libri 26 · World Scientific

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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 rather than on the relationship between different forcing axioms or their consistency strengths.

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Stevo Todorcevic is professor of mathematics at the University of Toronto and holds senior research positions at the CNRS in Paris and SANU in Belgrade. He is the author or coauthor of several books, including "Walks on Ordinals and Their Characteristics" and "Ramsey Methods in Analysis."