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Notes on forcing axioms /
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 boundedne...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Hackensack] New Jersey :
World Scientific,
[2014]
|
| Colección: | Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;
v. 26. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Todorcevic, Stevo, |e author. | |
| 245 | 1 | 0 | |a Notes on forcing axioms / |c 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. |
| 264 | 1 | |a [Hackensack] New Jersey : |b World Scientific, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (xiii, 219 pages). | ||
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| 490 | 1 | |a Lecture notes series (Institute for Mathematical Sciences, National University of Singapore) ; |v vol. 26 | |
| 504 | |a Includes bibliographical references (pages 217-219) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Forcing (Model theory) | |
| 650 | 0 | |a Axioms. | |
| 650 | 0 | |a Baire classes. | |
| 650 | 6 | |a Forcing (Théorie des modèles) | |
| 650 | 6 | |a Axiomes. | |
| 650 | 6 | |a Classes de Baire. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Axioms. |2 fast |0 (OCoLC)fst00824492 | |
| 650 | 7 | |a Baire classes. |2 fast |0 (OCoLC)fst00825536 | |
| 650 | 7 | |a Forcing (Model theory) |2 fast |0 (OCoLC)fst00931616 | |
| 655 | 7 | |a maxims. |2 aat | |
| 655 | 7 | |a aphorisms. |2 aat | |
| 655 | 7 | |a proverbs. |2 aat | |
| 655 | 7 | |a Sayings. |2 fast |0 (OCoLC)fst01920779 | |
| 655 | 7 | |a Sayings. |2 lcgft | |
| 655 | 7 | |a Proverbes. |2 rvmgf | |
| 700 | 1 | |a Chong, C.-T. |q (Chi-Tat), |d 1949- |e editor. | |
| 700 | 1 | |a Feng, Qi, |d 1955- |e editor. | |
| 700 | 1 | |a Yang, Yue, |d 1964- |e editor. | |
| 700 | 1 | |a Slaman, T. A. |q (Theodore Allen), |d 1954- |e editor. | |
| 700 | 1 | |a Woodin, W. H. |q (W. Hugh), |e editor. | |
| 776 | 0 | 8 | |i Print version: |a Todorcevic, Stevo. |t Notes on forcing axioms. |d New Jersey : World Scientific, 2014 |z 9789814571579 |w (DLC) 2013042520 |w (OCoLC)861554483 |
| 830 | 0 | |a Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; |v v. 26. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=689761 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a 1. Baire category theorem and the Baire category numbers. 1.1. The Baire category method - a classical example. 1.2. Baire category numbers. 1.3. P-clubs. 1.4. Baire category numbers of posets. 1.5. Proper and semi-proper posets -- 2. Coding sets by the real numbers. 2.1. Almost-disjoint coding. 2.2. Coding families of unordered pairs of ordinals. 2.3. Coding sets of ordered pairs. 2.4. Strong coding. 2.5. Solovay's lemma and its corollaries -- 3. Consequences in descriptive set theory. 3.1. Borel isomorphisms between Polish spaces. 3.2. Analytic and co-analytic sets. 3.3. Analytic and co-analytic sets under p > ω1 -- 4. Consequences in measure theory. 4.1. Measure spaces. 4.2. More on measure spaces -- 5. Variations on the Souslin hypothesis. 5.1. The countable chain condition. 5.2. The Souslin hypothesis. 5.3. A selective ultrafilter from m > ω1. 5.4. The countable chain condition versus the separability -- 6. The S-spaces and the L-spaces. 6.1. Hereditarily separable and hereditarily Lindelöf spaces. 6.2. Countable tightness and the S- and L-space problems -- 7. The side-condition method. 7.1. Elementary submodels as side conditions. 7.2. Open graph axiom -- 8. Ideal dichotomies. 8.1. Small ideal dichotomy. 8.2. Sparse set-mapping principle. 8.3. P-ideal dichotomy -- 9. Coherent and Lipschitz trees. 9.1. The Lipschitz condition. 9.2. Filters and trees. 9.3. Model rejecting a finite set of nodes. 9.4. Coloring axiomfor coherent trees -- 10. Applications to the S-space problem and the von Neumann problem. 10.1. The S-space problem and its relatives. 10.2. The P-ideal dichotomy and a problem of von Neumann -- 11. Biorthogonal systems. 11.1. The quotient problem. 11.2. A topological property of the dual ball. 11.3. A problem of Rolewicz. 11.4. Function spaces -- 12. Structure of compact spaces. 12.1. Covergence in topology. 12.2. Ultrapowers versus reduced powers. 12.3. Automatic continuity in Banach algebras -- 13. Ramsey theory on ordinals. 13.1. The arrow notation. 13.2. ω2[symbol]. 13.3. ω1[symbol] -- 14. Five cofinal types. 14.1. Tukey reductions and cofinal equivalence. 14.2. Directed posets of cardinality at most [symbol]. 14.3. Directed sets of cardinality continuum -- 15. Five linear orderings. 15.1. Basis problem for uncountable linear orderings. 15.2. Separable linear orderings. 15.3. Ordered coherent trees. 15.4. Aronszajn orderings -- 16. Cardinal arithmetic and mm. 16.1. mm and the continuum. 16.2. mm and cardinal arithmetic above the continuum -- 17. Reflection principles. 17.1. Strong reflection of stationary sets. 17.2. Weak reflection of stationary sets. 17.3. Open stationary set-mapping reflection. | |
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