Almost free modules: set-theoretic methods
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
North-Holland
1990
|
| Schriftenreihe: | North-Holland mathematical library
46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 481 S. |
| ISBN: | 0444885021 |
Internformat
MARC
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| 100 | 1 | |a Eklof, Paul C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Almost free modules |b set-theoretic methods |c Paul C. Eklof ; Alan H. Mekler |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1990 | |
| 300 | |a XVI, 481 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | TABLE OF CONTENTS
The numbers after each chapter indicate the chapters on which
it depends (where dependence is a transitive relation). Everything
depends on I and II.
I. ALGEBRAIC PRELIMINARIES
1. Homomorphisms and extensions 1
2. Direct sums and products 4
3. Linear topologies 11
II. SET THEORY
1. Ordinary set theory 16
2. Filters and large cardinals 22
3. Ultraproducts 29
4. Cubs and stationary sets 34
5. Games and trees 41
Exercises 45
Notes 50
III. SLENDER MODULES
1. Introduction to slenderness 51
2. Examples of slender modules and rings 58
3. The Los Eda theorem 65
Exercises 77
Notes 80
IV. ALMOST FREE MODULES
1. K free modules 82
2. Ni free abelian groups 91
3. Compactness results 102
Exercises 112
Notes 116
xiv CONTENTS
V. PURE INJECTIVE MODULES
1. Structure theory 118
2. Cotorsion groups 130
Exercises 135
Notes 137
VI. MORE SET THEORY
1. Prediction principles 138
2. Models of set theory 146
3. L, the constructible universe 153
4. MA and PFA 163
Exercises 175
Notes 178
VII. ALMOST FREE MODULES REVISITED (IV, VI)
1. /c free modules revisited 180
2. /c free abelian groups 187
3. Transversals and A systems 198
3A. Reshuffling A systems 209
4. Hereditarily separable groups 226
Exercises 238
Notes 245
VIII. COUNTABLY SEPARABLE GROUPS (VI, VII. 1)
1. Constructions and definitions 247
2. Ki separable groups under Martin s axiom 259
3. Ki separable groups under PFA 266
Exercises 272
Notes 274
IX. QUOTIENTS OF PRODUCTS OF THE INTEGERS
(HI, IV, V)
1. Perps and products 276
2. Countable products of the integers 282
CONTENTS xv
3. Uncountable products of the integers 286
4. Radicals and large cardinals 289
Exercises 296
Notes 299
X. ITERATED SUMS AND PRODUCTS (III)
1. The Reid class 300
2. Types in the Reid class 304
Exercises 311
Notes 311
XL TOPOLOGICAL METHODS (X, IV)
1. Inverse and direct limits 313
2. Completions 321
3. Density and dual bases 326
4. Groups of continuous functions 330
Exercises 340
Notes 342
XII. THE STRUCTURE OF EXT (VII, VIII.l)
1. The vanishing of Ext 344
2. The rank of Ext 355
3. Uniformization and W groups 367
Exercises 383
Notes 387
XIII. THE BLACK BOX AND ENDOMORPHISM RINGS
(V, VI)
1. Black Box 389
2. Proof of the Black Box 396
3. Endomorphism rings of cotorsion free groups 400
4. Endomorphism rings of separable groups 407
Exercises 415
Notes 418
xvi CONTENTS
XIV. DUAL GROUPS (IX, XI, XIII)
1. Invariants of dual groups 420
2. Tree groups 425
3. Criteria for being a dual group 430
4. Some non reflexive dual groups 435
5. More dual groups 443
Notes 452
OPEN PROBLEMS 453
BIBLIOGRAPHY 456
INDEX 477
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:49:06Z |
| institution | BVB |
| isbn | 0444885021 |
| language | English |
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| physical | XVI, 481 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | North-Holland |
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| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Eklof, Paul C. Verfasser aut Almost free modules set-theoretic methods Paul C. Eklof ; Alan H. Mekler Amsterdam [u.a.] North-Holland 1990 XVI, 481 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 46 Mengenlehre (DE-588)4074715-3 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Fast freier Modul (DE-588)4311199-3 gnd rswk-swf Modul (DE-588)4129770-2 s Mengenlehre (DE-588)4074715-3 s DE-604 Fast freier Modul (DE-588)4311199-3 s DE-188 Mekler, Alan H. Verfasser aut North-Holland mathematical library 46 (DE-604)BV000005206 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001759187&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eklof, Paul C. Mekler, Alan H. Almost free modules set-theoretic methods North-Holland mathematical library Mengenlehre (DE-588)4074715-3 gnd Modul (DE-588)4129770-2 gnd Fast freier Modul (DE-588)4311199-3 gnd |
| subject_GND | (DE-588)4074715-3 (DE-588)4129770-2 (DE-588)4311199-3 |
| title | Almost free modules set-theoretic methods |
| title_auth | Almost free modules set-theoretic methods |
| title_exact_search | Almost free modules set-theoretic methods |
| title_full | Almost free modules set-theoretic methods Paul C. Eklof ; Alan H. Mekler |
| title_fullStr | Almost free modules set-theoretic methods Paul C. Eklof ; Alan H. Mekler |
| title_full_unstemmed | Almost free modules set-theoretic methods Paul C. Eklof ; Alan H. Mekler |
| title_short | Almost free modules |
| title_sort | almost free modules set theoretic methods |
| title_sub | set-theoretic methods |
| topic | Mengenlehre (DE-588)4074715-3 gnd Modul (DE-588)4129770-2 gnd Fast freier Modul (DE-588)4311199-3 gnd |
| topic_facet | Mengenlehre Modul Fast freier Modul |
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