| Description |
1 online resource (vi, 934 pages) |
| Series |
De Gruyter series in logic and its applications, 1438-1893 ; 1 |
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De Gruyter series in logic and its applications ; 1. 1438-1893
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| Contents |
880-01 1 Introduction -- 1.1 The Nonstationary Ideal On Ï?1 -- 1.2 The Partial Order â??max -- 1.3 â??max Variations -- 1.4 Extensions Of Inner Models Beyond L (â??) -- 1.5 Concluding Remarks -- 2 Preliminaries -- 2.1 Weakly Homogeneous Trees And Scales -- 2.2 Generic Absoluteness -- 2.3 The Stationary Tower -- 2.4 Forcing Axioms -- 2.5 Reflection Principles -- 2.6 Generic Ideals -- 3 The Nonstationary Ideal -- 3.1 The Nonstationary Ideal And Î?Ì°12 -- 3.2 The Nonstationary Ideal And Ch -- 4 The â??max-Extension -- 4.1 Iterable Structures |
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880-01/(S Frontmatter -- 1 Introduction -- 2 Preliminaries -- 3 The nonstationary ideal -- 4 The ℙmax-extension -- 5 Applications -- 6 ℙmax variations. 6.1 2ℙmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.1 ℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.2 ℚ*max -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.3 2ℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.4 Weak Kurepa trees and ℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.5 KTℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.6 Null sets and the nonstationary ideal -- 6 ℙmax variations. 6.3 Nonregular ultrafilters on ω1 -- 7 Conditional variations -- 8 ♣ principles for ω1. 8.1 Condensation Principles -- 8 ♣ principles for ω1. 8.2 ℙ♣NSmax -- 8 ♣ principles for ω1. 8.3 The principles, ♣+NS and ♣++NS -- 9 Extensions of L(Γ, ℝ). 9.1 AD+ -- 9 Extensions of L(Γ, ℝ). 9.2 The ℙmax-extension of L(Γ, ℝ) -- 9 Extensions of L(Γ, ℝ). 9.3 The ℚmax-extension of L(Γ, ℝ) -- 9 Extensions of L(Γ, ℝ). 9.4 Chang's Conjecture -- 9 Extensions of L(Γ, ℝ). 9.5 Weak and Strong Reflection Principles -- 9 Extensions of L(Γ, ℝ). 9.6 Strong Chang's Conjecture -- 9 Extensions of L(Γ, ℝ). 9.7 Ideals on ω2 -- 10 Further results. 10.1 Forcing notions and large cardinals -- 10 Further results. 10.2 Coding into L(P(ω1)) -- 10 Further results. 10.3 Bounded forms of Martin's Maximum -- 10 Further results. 10.4 Ω-logic -- 10 Further results. 10.5 Ω-logic and the Continuum Hypothesis -- 10 Further results. 10.6 The Axiom (*)+ -- 10 Further results. 10.7 The Effective Singular Cardinals Hypothesis -- 11 Questions -- Bibliography -- Index |
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4.2 The Partial Order â??max 5 Applications -- 5.1 The Sentence Ï?ac -- 5.2 Martinâ€?S Maximum, Ï?ac And â??Ï?(Ï?2) -- 5.3 The Sentence Ï?ac -- 5.4 The Stationary Tower And â??max -- 5.5 â??*Max -- 5.6 â??0Max -- 5.7 The Axiom (**) -- 5.8 Homogeneity Properties Of P(Ï?1)/Lns -- 6 â??max Variations -- 6.1 2â??max -- 6.2 Variations For Obtaining Ï?1-Dense Ideals -- 6.3 Nonregular Ultrafilters On Ï?1 -- 7 Conditional Variations -- 7.1 Suslin Trees -- 7.2 The Borel Conjecture -- 8 â?£ Principles For Ï?1 -- 8.1 Condensation Principles |
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8.2 â??â?£Nsmax 8.3 The Principles, â?£+Ns And â?£++Ns -- 9 Extensions Of L(Î?, â??) -- 9.1 Ad+ -- 9.2 The â??max-Extension Of L(Î?, â??) -- 9.3 The â?šmax-Extension Of L(Î?, â??) -- 9.4 Changâ€?S Conjecture -- 9.5 Weak And Strong Reflection Principles -- 9.6 Strong Changâ€?S Conjecture -- 9.7 Ideals On Ï?2 -- 10 Further Results -- 10.1 Forcing Notions And Large Cardinals -- 10.2 Coding Into L(P(Ï?1)) -- 10.3 Bounded Forms Of Martinâ€?S Maximum -- 10.4 Ω-Logic -- 10.5 Ω-Logic And The Continuum Hypothesis -- 10.6 The Axiom (*)+ |
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10.7 The Effective Singular Cardinals Hypothesis 11 Questions -- Bibliography -- Index |
| Bibliography |
Includes bibliographical references (pages 927-929) and index |
| Notes |
Print version record |
| Subject |
Forcing (Model theory)
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MATHEMATICS -- General.
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Forcing (Model theory)
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Lógica matemática.
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Teoria dos conjuntos.
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| Form |
Electronic book
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| ISBN |
9783110804737 |
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3110804735 |
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