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Notes on forcing axioms

Author: Stevo TodorcevicC -T ChongQi FengYue YangT A SlamanAll authors
Publisher: [Hackensack] New Jersey : World Scientific, [2014] ©2014
Series: Lecture notes series (National University of Singapore. Institute for Mathematical Sciences), v. 26.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Todorcevic, Stevo.
Notes on forcing axioms.
New Jersey : World Scientific, 2014
(DLC) 2013042520
(OCoLC)861554483
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Stevo Todorcevic; C -T Chong; Qi Feng; Yue Yang; T A Slaman; W H Woodin
ISBN: 9789814571586 981457158X 9781306396578 1306396573
OCLC Number: 869457463
Description: 1 online resource (xiii, 219 pages).
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.
Series Title: Lecture notes series (National University of Singapore. Institute for Mathematical Sciences), v. 26.
Responsibility: 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.

Abstract:

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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