The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal.
Woodin, W. Hugh.
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal. - 1st ed. - 1 online resource (944 pages) - De Gruyter Series in Logic and Its Applications Series ; v.1 . - De Gruyter Series in Logic and Its Applications Series .
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.
No detailed description available for "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal".
9783110804737
Forcing (Model theory).
Model theory.
Electronic books.
QA9.7.W66 1999eb
511.3
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal. - 1st ed. - 1 online resource (944 pages) - De Gruyter Series in Logic and Its Applications Series ; v.1 . - De Gruyter Series in Logic and Its Applications Series .
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.
No detailed description available for "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal".
9783110804737
Forcing (Model theory).
Model theory.
Electronic books.
QA9.7.W66 1999eb
511.3