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.

Publication Info.	[Hackensack] New Jersey : World Scientific, [2014]
	©2014

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Description	1 online resource (xiii, 219 pages).
Physical Medium	polychrome
Description	text file
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.
Bibliography	Includes bibliographical references (pages 217-219) and index.
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.
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.
Local Note	eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject	Forcing (Model theory)
	Forcing (Model theory)
	Axioms.
	Axioms.
	Baire classes.
	Baire classes.
Genre/Form	Electronic books.
	Electronic books.
Added 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.
Other Form:	Print version: Todorcevic, Stevo. Notes on forcing axioms. New Jersey : World Scientific, 2014 9789814571579 (DLC) 2013042520 (OCoLC)861554483
ISBN	9789814571586 (electronic book)
	981457158X (electronic book)
	9781306396578
	1306396573
	9789814571579
	9814571571

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.

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