Proper and improper forcing:
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| Previous Title: | Proper forcing |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1998
|
| Edition: | 2. ed. |
| Series: | Perspectives in mathematical logic
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XLVII, 1020 S. |
| ISBN: | 3540517006 |
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MARC
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| 100 | 1 | |a Shelah, Saharon |d 1945- |e Verfasser |0 (DE-588)120062755 |4 aut | |
| 245 | 1 | 0 | |a Proper and improper forcing |c Saharon Shelah |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XLVII, 1020 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Perspectives in mathematical logic | |
| 650 | 4 | |a Axiomatic set theory | |
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| 780 | 0 | 0 | |i 1. Auflage |t Proper forcing |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Introduction xv
Notation xxi
Content by Subject xxiii
Annotated Content xxviii
I. Forcing, Basic Facts 1
§0. Introduction 1
§1. Introducing Forcing 2
§2. The Consistency of CH (The Continuum Hypothesis) 11
§3. On the Consistency of the Failure of CH 17
§4. More on the Cardinality 2N° and Cohen Reals 23
§5. Equivalence of Forcings Notions, and Canonical Names 28
§6. Random Reals, Collapsing Cardinals and Diamonds 35
§7. * Does Not Imply 0 41
II. Iteration of Forcing 50
§0. Introduction 50
§1. The Composition of Two Forcing Notions 51
§2. Iterated Forcing 57
§3. Martin s Axiom and Few Applications 63
§4. The Uniformization Property 72
§5. Maximal Almost Disjoint Families of Subsets of w 83
x Table of Contents
III. Proper Forcing 89
§0. Introduction 89
§1. Introducing Properness 90
§2. More on Properness 98
§3. Preservation of Properness Under Countable Support Iteration 107
§4. Martin s Axiom Revisited 117
§5. On Aronszajn Trees 123
§6. Maybe There Is No K2 Aronszajn Tree 127
§7. Closed Unbounded Subsets of wi Can Run Away from Many Sets 133
§8. The Consistency of SH + CH + There Are No Kurepa Trees 137
IV. On Oracle c.c, the Lifting Problem of the Measure Algebra,
and P(a )/finite Has No Non trivial Automorphism 144
§0. Introduction 144
§1. On Oracle Chain Conditions 148
§2. The Omitting Type Theorem 153
§3. Iterations of M c.c. Forcings 156
§4. The Lifting Problem of the Measure Algebra 161
§5. Automorphisms of ¦p(w)/finite 171
§6. Proof of Main Lemma 5.6 175
V. o Properness and Not Adding Reals 194
§0. Introduction 194
§1. 5 Completeness a Sufficient Condition for Not Adding Reals 196
§2. Generalizations of Properness 206
§3. a Properness and (£, a) Properness Revisited 212
§4. Preservation of w Properness + the ^w Bounding Property 216
§5. Which Forcings Can We Iterate Without Adding Reals 224
§6. Specializing an Aronszajn Tree Without Adding Reals 228
§7. Iteration of (£, O) Complete Forcing Notions 237
§8. The Consistency of SH + CH + There Are No Kurepa Trees 241
Table of Contents xi
VI. Preservation of Additional Properties, and Applications 247
§1. A General Preservation Theorem 252
§2. Examples 278
§3. Preservation of Unboundedness 309
§4. There May Be No P Point 325
§5. There May Exist a Unique Ramsey Ultrafilter 335
§6. On the Splitting Number s and Domination Number b and on a 346
§7. On s b = a 362
§8. On t) s = b 366
VII. Axioms and Their Application 372
§0. Introduction 372
§1. On the K Chain Condition, When Reals Are Not Added 372
§2. The Axioms 377
§3. Applications of Axiom II (so CH Holds) 383
§4. Applications of Axiom I 398
§5. A Counterexample Connected to Preservation 400
VIII. K pic and Not Adding Reals 403
§0. Introduction 403
§1. Mixed Iteration N2 c.c, N2 Complete 404
§2. Chain Conditions Revisited 409
§3. The Axioms Revisited 414
§4. More on Forcing Not Adding w Sequences
and on the Diagonal Argument 418
IX. Souslin Hypothesis Does Not Imply
Every Aronszajn Tree Is Special 436
§0. Introduction 436
§1. Free Limits 436
§2. Preservation by Free Limit 439
xii Table of Contents
§3. Aronszajn Trees: Various Ways to Specialize 443
§4. Independence Results 452
X. On Semi Proper Forcing 467
§0. Introduction 467
§1. Iterated Forcing with RCS
(Revised Countable Support) 468
§2. Proper Forcing Revisited 482
§3. Pseudo Completeness 491
§4. Specific Forcings 499
§5. Chain Conditions and Abraham s Problem 510
§6. Reflection Properties of S $:
Refining Abraham s Problem and Precipitous Ideals 513
§7. Friedman s Problem 524
XI. Changing Cofinalities; Equi Consistency Results 532
§0. Introduction 532
§1. The Theorems 532
§2. The Condition 542
§3. The Preservation Properties Guaranteed by the 5 Condition 546
§4. Forcing Notions Satisfying the 5 Condition 550
§5. Finite Composition 558
§6. Preservation of the I Condition by Iteration 562
§7. Further Independence Results 576
§8. Relativising to a Stationary Set 586
XII. Improper Forcing 589
§0. Introduction 589
§1. Games and Properness 590
§2. When Is Namba Forcing Semiproper, Chang s Conjecture
and Games 597
Table of Contents xiii
XIII. Large Ideals on u i 604
§0. Introduction 604
§1. Semi Stationarity 609
§2. 5 Suitable Iterations and Sealing Forcing 622
§3. On 7 (u i)/PWl Being Layered or the Levy Algebra 637
§4. V{wi)/{VUi + S) is Reflective or Ulam 656
XIV. Iterated Forcing with Uncountable Support 679
§0. Introduction 679
§1. K Revised Support Iteration 680
§2. Pseudo Completeness 688
§3. Axioms 715
§4. On Sacks Forcing 720
§5. Abraham s Second Problem Iterating Changing Cofinality tow 722
XV. A More General Iterable Condition Ensuring
Nx Is Not Collapsed 732
§0. Introduction 732
§1. Preliminaries 733
§2. Trees of Models and UP 735
§3. Preservation of the UP{1,S, W) by Iteration 761
§4. Families of Ideals and Families of Partial Orders 769
XVI. Large Ideals on Ni from Smaller Cardinals 778
§0. Introduction 778
§1. Bigness of Stationary T C S n0 (A) 778
§2. Getting Large Ideals on b^ 785
XVII. Forcing Axioms 803
§0. Introduction 803
§1. Semiproper Forcing Axiom Implies Martin s Maximum 804
§2. SPFA Does Not Imply PFA+ 809
xiv Table of Contents
§3. Canonical Functions for wi 829
§4. A Largeness of TJ0Jl in Forcing Extensions of L
and Canonical Functions 839
XVIII. More on Proper Forcing 854
§0. Introduction 854
§1. No New Reals: A Counterexample and New Questions 855
§2. Not Adding Reals 867
§3. Other Preservations 888
§4. There May Be a Unique P Point 932
Appendix. On Weak Diamonds and the Power of Ext 940
§0. Introduction 940
§1. Unif: a Strong Negation of the Weak Diamond 942
§2. On the Power of Ext and Whitehead s Problem 961
§3. Weak Diamond for H2 Assuming CH 982
References 997
More References 1012
|
| any_adam_object | 1 |
| author | Shelah, Saharon 1945- |
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:13:19Z |
| institution | BVB |
| isbn | 3540517006 |
| language | English |
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| physical | XLVII, 1020 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Springer |
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| series2 | Perspectives in mathematical logic |
| spelling | Shelah, Saharon 1945- Verfasser (DE-588)120062755 aut Proper and improper forcing Saharon Shelah 2. ed. Berlin [u.a.] Springer 1998 XLVII, 1020 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematical logic Axiomatic set theory Forcing (Model theory) Axiomatische Mengenlehre (DE-588)4143743-3 gnd rswk-swf Forcing (DE-588)4154978-8 gnd rswk-swf Forcing (DE-588)4154978-8 s Axiomatische Mengenlehre (DE-588)4143743-3 s DE-604 1. Auflage Proper forcing HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007848479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shelah, Saharon 1945- Proper and improper forcing Axiomatic set theory Forcing (Model theory) Axiomatische Mengenlehre (DE-588)4143743-3 gnd Forcing (DE-588)4154978-8 gnd |
| subject_GND | (DE-588)4143743-3 (DE-588)4154978-8 |
| title | Proper and improper forcing |
| title_auth | Proper and improper forcing |
| title_exact_search | Proper and improper forcing |
| title_full | Proper and improper forcing Saharon Shelah |
| title_fullStr | Proper and improper forcing Saharon Shelah |
| title_full_unstemmed | Proper and improper forcing Saharon Shelah |
| title_old | Proper forcing |
| title_short | Proper and improper forcing |
| title_sort | proper and improper forcing |
| topic | Axiomatic set theory Forcing (Model theory) Axiomatische Mengenlehre (DE-588)4143743-3 gnd Forcing (DE-588)4154978-8 gnd |
| topic_facet | Axiomatic set theory Forcing (Model theory) Axiomatische Mengenlehre Forcing |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007848479&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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