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...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , , , , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Hackensack] New Jersey :
World Scientific,
[2014]
|
| Schriftenreihe: | Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;
v. 26. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xiii, 219 pages). |
| Bibliographie: | Includes bibliographical references (pages 217-219) and index. |
| ISBN: | 9789814571586 981457158X 9781306396578 1306396573 |
Internformat
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| 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. | |
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| 700 | 1 | |a Feng, Qi, |d 1955- |e editor. |1 https://id.oclc.org/worldcat/entity/E39PCjt8RRDKQtWtpGq6ktBqXq |0 http://id.loc.gov/authorities/names/n2013062387 | |
| 700 | 1 | |a Yang, Yue, |d 1964- |e editor. |1 https://id.oclc.org/worldcat/entity/E39PCjK93rHv8x4TBgygGXHGMd |0 http://id.loc.gov/authorities/names/n2013063346 | |
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| 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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| author | Todorcevic, Stevo |
| author2 | Chong, C.-T. (Chi-Tat), 1949- Feng, Qi, 1955- Yang, Yue, 1964- Slaman, T. A. (Theodore Allen), 1954- Woodin, W. H. (W. Hugh) |
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| author_facet | Todorcevic, Stevo Chong, C.-T. (Chi-Tat), 1949- Feng, Qi, 1955- Yang, Yue, 1964- Slaman, T. A. (Theodore Allen), 1954- Woodin, W. H. (W. Hugh) |
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| 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. |
| ctrlnum | (OCoLC)869457463 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| discipline | Mathematik |
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Institute for Mathematical Sciences) ;</subfield><subfield code="v">v. 26.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2003042729</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=689761</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="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. 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| genre | maxims. aat aphorisms. aat proverbs. aat Sayings fast Sayings. lcgft http://id.loc.gov/authorities/genreForms/gf2014026170 Proverbes. rvmgf |
| genre_facet | maxims. aphorisms. proverbs. Sayings Sayings. Proverbes. |
| id | ZDB-4-EBA-ocn869457463 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:46Z |
| institution | BVB |
| isbn | 9789814571586 981457158X 9781306396578 1306396573 |
| language | English |
| oclc_num | 869457463 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 219 pages). |
| psigel | ZDB-4-EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific, |
| record_format | marc |
| series | Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; |
| series2 | Lecture notes series (Institute for Mathematical Sciences, National University of Singapore) ; |
| spelling | Todorcevic, Stevo, author. http://id.loc.gov/authorities/names/n87874475 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. [Hackensack] New Jersey : World Scientific, [2014] ©2014 1 online resource (xiii, 219 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture notes series (Institute for Mathematical Sciences, National University of Singapore) ; vol. 26 Includes bibliographical references (pages 217-219) and index. Print version record. 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. 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. Forcing (Model theory) http://id.loc.gov/authorities/subjects/sh85050461 Axioms. http://id.loc.gov/authorities/subjects/sh85010589 Baire classes. http://id.loc.gov/authorities/subjects/sh93007179 Forcing (Théorie des modèles) Axiomes. Classes de Baire. MATHEMATICS General. bisacsh Axioms fast Baire classes fast Forcing (Model theory) fast maxims. aat aphorisms. aat proverbs. aat Sayings fast Sayings. lcgft http://id.loc.gov/authorities/genreForms/gf2014026170 Proverbes. rvmgf Chong, C.-T. (Chi-Tat), 1949- editor. https://id.oclc.org/worldcat/entity/E39PBJt8m4PHhJYfHR4DGBDpfq http://id.loc.gov/authorities/names/n83161355 Feng, Qi, 1955- editor. https://id.oclc.org/worldcat/entity/E39PCjt8RRDKQtWtpGq6ktBqXq http://id.loc.gov/authorities/names/n2013062387 Yang, Yue, 1964- editor. https://id.oclc.org/worldcat/entity/E39PCjK93rHv8x4TBgygGXHGMd http://id.loc.gov/authorities/names/n2013063346 Slaman, T. A. (Theodore Allen), 1954- editor. https://id.oclc.org/worldcat/entity/E39PBJyRFPwqHtVHh34KHtkVYP http://id.loc.gov/authorities/names/n88271514 Woodin, W. H. (W. Hugh), editor. https://id.oclc.org/worldcat/entity/E39PBJdrHdBXMDfgQmMjd8gHYP http://id.loc.gov/authorities/names/n86039104 has work: Notes on forcing axioms (Text) https://id.oclc.org/worldcat/entity/E39PCFJRydfmbwVTWjc8fK8dXq https://id.oclc.org/worldcat/ontology/hasWork Print version: Todorcevic, Stevo. Notes on forcing axioms. New Jersey : World Scientific, 2014 9789814571579 (DLC) 2013042520 (OCoLC)861554483 Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; v. 26. http://id.loc.gov/authorities/names/no2003042729 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=689761 Volltext 505-00/(S 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. |
| spellingShingle | Todorcevic, Stevo Notes on forcing axioms / Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; 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. Forcing (Model theory) http://id.loc.gov/authorities/subjects/sh85050461 Axioms. http://id.loc.gov/authorities/subjects/sh85010589 Baire classes. http://id.loc.gov/authorities/subjects/sh93007179 Forcing (Théorie des modèles) Axiomes. Classes de Baire. MATHEMATICS General. bisacsh Axioms fast Baire classes fast Forcing (Model theory) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85050461 http://id.loc.gov/authorities/subjects/sh85010589 http://id.loc.gov/authorities/subjects/sh93007179 http://id.loc.gov/authorities/genreForms/gf2014026170 |
| title | Notes on forcing axioms / |
| title_auth | Notes on forcing axioms / |
| title_exact_search | Notes on forcing axioms / |
| title_full | 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. |
| title_fullStr | 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. |
| title_full_unstemmed | 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. |
| title_short | Notes on forcing axioms / |
| title_sort | notes on forcing axioms |
| topic | Forcing (Model theory) http://id.loc.gov/authorities/subjects/sh85050461 Axioms. http://id.loc.gov/authorities/subjects/sh85010589 Baire classes. http://id.loc.gov/authorities/subjects/sh93007179 Forcing (Théorie des modèles) Axiomes. Classes de Baire. MATHEMATICS General. bisacsh Axioms fast Baire classes fast Forcing (Model theory) fast |
| topic_facet | Forcing (Model theory) Axioms. Baire classes. Forcing (Théorie des modèles) Axiomes. Classes de Baire. MATHEMATICS General. Axioms Baire classes maxims. aphorisms. proverbs. Sayings Sayings. Proverbes. |
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