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Author Todorcevic, Stevo, author.

Title Notes on forcing axioms / Stevo Todorcevic, University of Toronto, Canada ; editors, Chitat Chong, Qi Feng, Yue Yang, National University of Singapore, Singapore, Theodore A. Slaman, W Hugh Woodin, University of California, Berkeley, USA
Published [Hackensack] New Jersey : World Scientific, [2014]


Description 1 online resource (xiii, 219 pages)
Series Lecture notes series (Institute for Mathematical Sciences, National University of Singapore) ; vol. 26
Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; v. 26.
Contents 1. Baire category theorem and the Baire category numbers -- 2. Coding sets by the real numbers -- 3. Consequences in descriptive set theory -- 4. Consequences in measure theory -- 5. Variations on the Souslin hypothesis -- 6. The S-s-paces and the L-spaces -- 7. The side-condition method -- 8. Ideal dichotomies -- 9. Coherent and Lipschitz trees -- 10. Applications to the S-space problem and the von Neumann problem -- 11. Biorthogonal systems -- 12. Structure of compact spaces -- 13. Ramsey theory on ordinals -- 14. Five cofinal types -- 15. Five linear orderings -- 16. Cardinal arithmetic and mm -- 17. Reflection principles
Summary 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
Bibliography Includes bibliographical references (pages 217-219) and index
Notes Print version record
Subject Forcing (Model theory)
Baire classes.
Baire classes.
Forcing (Model theory)
Genre/Form maxims.
Form Electronic book
Author Chong, C.-T. (Chi-Tat), 1949- editor.
Feng, Qi, 1955- editor.
Yang, Yue, 1964- editor.
Slaman, T. A. (Theodore Allen), 1954- editor.
Woodin, W. H. (W. Hugh), editor.
ISBN 9789814571586