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The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal.

By: Series: De Gruyter Series in Logic and Its Applications SerPublisher: Berlin/Boston : De Gruyter, Inc., 1999Copyright date: ©1999Description: 1 online resource (944 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110804737
Subject(s): Genre/Form: Additional physical formats: Print version:: The Axiom of Determinacy, Forcing Axioms, and the Nonstationary IdealDDC classification:
  • 511.3
LOC classification:
  • QA9.7.W66 1999eb
Online resources:
Contents:
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.
Summary: The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF-N00019767
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP-N00019767
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

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.

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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