Analytic quotients : theory of liftings for quotients over analytic ideals on the integers / / Ilijas Farah

• Autore: Farah Ilijas <1966->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2000]; ©2000
• Descrizione fisica: 1 online resource (201 p.)
• Disciplina: 510 s; 511.3/22
• Soggetto topico: Set theory; Algebra, Boolean; Lifting theory
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""Contents""; ""Preface""; ""Acknowledgments""; ""A note to the reader""; ""Introduction""; ""Chapter 1. Baire-measurable homomorphisms of analytic quotients""; ""1.1. Introduction""; ""1.2. Ideals induced by submeasures""; ""1.3. Preorderings on analytic quotients""; ""1.4. The Radonâ€?Nikodym property""; ""1.5. Asymptotically additive liftings""; ""1.6. The Radonâ€?Nikodym property of Fin and Fin x0""; ""1.7. A reformulation of Todorcevic's hypothesis""; ""1.8. Approximate homomorphisms and non-pathological submeasures""; ""1.9. The lifting theorem and the non-lifting theorem"" ; ""1.10. Permanence properties of quotients""""1.11. Simple FÏ? P-ideals which are not summable""; ""1.12. The structure of summable ideals""; ""1.13. The structure of density ideals""; ""1.14. Remarks and questions""; ""Chapter 2. Open Coloring Axiom and uniformization""; ""2.1. Why Open Coloring Axiom?""; ""2.2. Coherent families of partial functions""; ""2.3. Coherent families of partitions""; ""2.4. â??[sub(2)]-reflection for coherent families""; ""2.5. Remarks and questions""; ""Chapter 3. Homomorphisms of analytic quotients under OCA""; ""3.1. Introduction"" ; ""3.2. Homomorphisms without Baire-measurable liftings""""3.3. Almost liftings and lifting theorems""; ""3.4. Applications: rigidity of analytic quotients""; ""3.5. Applications: quotients embeddable into analytic quotients""; ""3.6. Automorphism groups""; ""3.7. Homogeneity of analytic quotients""; ""3.8. Almost liftings of embeddings into P(N)/Fin""; ""3.9. Almost liftings of embeddings into P(N[sup(2)])/Fin x0""; ""3.10. Nonmeager hereditary sets""; ""3.11. Approximate homomorphisms; more on stabilizers""; ""3.12. A local version of the OCA lifting theorem"" ; ""3.13. The proof of the OCA lifting theorem for the analytic P-ideals""""3.14. Remarks and questions""; ""Chapter 4. Weak Extension Principle""; ""4.1. Introduction""; ""4.2. Dependence of functions on their variables""; ""4.3. Prime mappings""; ""4.4. Autohomeomorphisms of finite powers of β[sub(w)] and w*""; ""4.5. Cechâ€?Stone remainders of countable ordinals""; ""4.6. Some Parovicenko spaces under wEP""; ""4.7. Remainders of locally compact, countable spaces""; ""4.8. Almost liftings and duality""; ""4.9. OCA and MA imply wEP""; ""4.10. Versions of wEP""; ""4.11. Remarks and questions"" ; ""Chapter 5. Gaps and limits in analytic quotients""""5.1. Introduction""; ""5.2. Gaps in the quotient over Fin""; ""5.3. Gaps in the quotient over 0 x Fin""; ""5.4. Gaps in the quotient over Fin x0""; ""5.5. The Todorcevic separation property, TSP""; ""5.6. Tukey reductions of nonlinear gaps""; ""5.7. TSP in quotients over analytic P-ideals""; ""5.8. Quotients as reduced products""; ""5.9. Preservation of gaps""; ""5.10. An analytic Hausdorff gap""; ""5.11. Limits in analytic quotients""; ""5.12. A coherent family of functions""; ""5.13. Remarks and questions""; ""Bibliography""; ""Index"" ; ""A""
• Titolo autorizzato: Analytic quotients
• ISBN: 1-4704-0293-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788841703321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; no. 702.