TY  - BOOK
AU  - Woodin,W.Hugh
TI  - The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
T2  - De Gruyter Series in Logic and Its Applications Series
SN  - 9783110804737
AV  - QA9.7.W66 1999eb 
U1  - 511.3 
PY  - 1999///
CY  - Berlin/Boston
PB  - De Gruyter, Inc.
KW  - Forcing (Model theory)
KW  - Model theory
KW  - Electronic books
N1  - Intro -- 1 Introduction -- 1.1 The Nonstationary Ideal On ω1 -- 1.2 The Partial Order ℙmax -- 1.3 ℙmax Variations -- 1.4 Extensions Of Inner Models Beyond L (ℝ) -- 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 δ̰12 -- 3.2 The Nonstationary Ideal And Ch -- 4 The ℙmax-Extension -- 4.1 Iterable Structures -- 4.2 The Partial Order ℙmax -- 5 Applications -- 5.1 The Sentence φac -- 5.2 Martin'S Maximum, φac And ◇ω(ω2) -- 5.3 The Sentence ψac -- 5.4 The Stationary Tower And ℙmax -- 5.5 ℙ*Max -- 5.6 ℙ0Max -- 5.7 The Axiom (**) -- 5.8 Homogeneity Properties Of P(ω1)/Lns -- 6 ℙmax Variations -- 6.1 2ℙmax -- 6.2 Variations For Obtaining ω1-Dense Ideals -- 6.3 Nonregular Ultrafilters On ω1 -- 7 Conditional Variations -- 7.1 Suslin Trees -- 7.2 The Borel Conjecture -- 8 ♣ Principles For ω1 -- 8.1 Condensation Principles -- 8.2 ℙ♣Nsmax -- 8.3 The Principles, ♣+Ns And ♣++Ns -- 9 Extensions Of L(Γ, ℝ) -- 9.1 Ad+ -- 9.2 The ℙmax-Extension Of L(Γ, ℝ) -- 9.3 The ℚmax-Extension Of L(Γ, ℝ) -- 9.4 Chang'S Conjecture -- 9.5 Weak And Strong Reflection Principles -- 9.6 Strong Chang'S Conjecture -- 9.7 Ideals On ω2 -- 10 Further Results -- 10.1 Forcing Notions And Large Cardinals -- 10.2 Coding Into L(P(ω1)) -- 10.3 Bounded Forms Of Martin'S Maximum -- 10.4 Ω-Logic -- 10.5 Ω-Logic And The Continuum Hypothesis -- 10.6 The Axiom (*)+ -- 10.7 The Effective Singular Cardinals Hypothesis -- 11 Questions -- Bibliography -- Index
N2  - No detailed description available for "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal"
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3044462
ER  -