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

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Bibliographic Details
Main Author:	Farah, Ilijas 1966- (Author)
Format:	Book
Language:	English
Published:	Providence, RI American Mathematical Society 2000
Series:	American Mathematical Society: Memoirs of the American Mathematical Society 702
Subjects:	Booleaanse algebra Teoria dos conjuntos Verzamelingen (wiskunde) Algebra, Boolean Lifting theory Set theory
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009184250&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Volume 148, Number 702 (second of 5 numbers)
Physical Description:	XVI, 177 S.
ISBN:	0821821172

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adam_text	Contents Preface xiii Acknowledgments xv A note to the reader xv Introduction 1 Chapter 1. Baire measurable homomorphisms of analytic quotients 5 1.1. Introduction 5 1.2. Ideals induced by submeasures 7 1.3. Preorderings on analytic quotients 11 1.4. The Radon Nikodym property 14 1.5. Asymptotically additive liftings 16 1.6. The Radon Nikodym property of Fin and Fin x 0 19 1.7. A reformulation of Todorcevic s hypothesis 20 1.8. Approximate homomorphisms and non pathological submeasures 25 1.9. The lifting theorem and the non lifting theorem 31 1.10. Permanence properties of quotients 32 1.11. Simple Fa P ideals which are not summable 33 1.12. The structure of summable ideals 34 1.13. The structure of density ideals 41 1.14. Remarks and questions 51 Chapter 2. Open Coloring Axiom and uniformization 55 2.1. Why Open Coloring Axiom? 56 2.2. Coherent families of partial functions 59 2.3. Coherent families of partitions 63 2.4. E2 reflection for coherent families 65 2.5. Remarks and questions 66 Chapter 3. Homomorphisms of analytic quotients under OCA 69 3.1. Introduction 69 3.2. Homomorphisms without Baire measurable liftings 71 3.3. Almost liftings and lifting theorems 72 3.4. Applications: rigidity of analytic quotients 74 3.5. Applications: quotients embeddable into analytic quotients 76 3.6. Automorphism groups 78 3.7. Homogeneity of analytic quotients 83 3.8. Almost liftings of embeddings into V{N)/ Fin 85 3.9. Almost liftings of embeddings into P(N2)/ Fin x0 90 3.10. Nonmeager hereditary sets 91 ix x CONTENTS 3.11. Approximate homomorphisms; more on stabilizers 92 3.12. A local version of the OCA lifting theorem 99 3.13. The proof of the OCA lifting theorem for the analytic P ideals 106 3.14. Remarks and questions 114 Chapter 4. Weak Extension Principle 117 4.1. Introduction 117 4.2. Dependence of functions on their variables 118 4.3. Prime mappings 120 4.4. Autohomeomorphisms of finite powers of /3w and w* 123 4.5. Cech Stone remainders of countable ordinals 124 4.6. Some Parovicenko spaces under wEP 126 4.7. Remainders of locally compact, countable spaces 130 4.8. Almost liftings and duality 132 4.9. OCA and MA imply wEP 135 4.10. Versions of wEP 139 4.11. Remarks and questions 140 Chapter 5. Gaps and limits in analytic quotients 143 5.1. Introduction 143 5.2. Gaps in the quotient over Fin 144 5.3. Gaps in the quotient over 0 x Fin 147 5.4. Gaps in the quotient over Fin x0 148 5.5. The Todorcevic separation property, TSP 151 5.6. Tukey reductions of nonlinear gaps 153 5.7. TSP in quotients over analytic P ideals 155 5.8. Quotients as reduced products 157 5.9. Preservation of gaps 160 5.10. An analytic Hausdorff gap 161 5.11. Limits in analytic quotients 164 5.12. A coherent family of functions 164 5.13. Remarks and questions 165 Bibliography 167 Index 172 Index of special symbols 176
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spellingShingle	Farah, Ilijas 1966- Analytic quotients theory of liftings for quotients over analytic ideals on the integers American Mathematical Society: Memoirs of the American Mathematical Society Booleaanse algebra gtt Teoria dos conjuntos larpcal Verzamelingen (wiskunde) gtt Algebra, Boolean Lifting theory Set theory
title	Analytic quotients theory of liftings for quotients over analytic ideals on the integers
title_auth	Analytic quotients theory of liftings for quotients over analytic ideals on the integers
title_exact_search	Analytic quotients theory of liftings for quotients over analytic ideals on the integers
title_full	Analytic quotients theory of liftings for quotients over analytic ideals on the integers Ilijas Farah
title_fullStr	Analytic quotients theory of liftings for quotients over analytic ideals on the integers Ilijas Farah
title_full_unstemmed	Analytic quotients theory of liftings for quotients over analytic ideals on the integers Ilijas Farah
title_short	Analytic quotients
title_sort	analytic quotients theory of liftings for quotients over analytic ideals on the integers
title_sub	theory of liftings for quotients over analytic ideals on the integers
topic	Booleaanse algebra gtt Teoria dos conjuntos larpcal Verzamelingen (wiskunde) gtt Algebra, Boolean Lifting theory Set theory
topic_facet	Booleaanse algebra Teoria dos conjuntos Verzamelingen (wiskunde) Algebra, Boolean Lifting theory Set theory
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009184250&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV008000141
work_keys_str_mv	AT farahilijas analyticquotientstheoryofliftingsforquotientsoveranalyticidealsontheintegers

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