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

W. Hugh Woodin

Published by De Gruyter 1999

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

W. Hugh Woodin

Volume 1 in the series De Gruyter Series in Logic and Its Applications

https://doi.org/10.1515/9783110804737

Contents

Frontmatter Publicly Available Download PDF	I
1 Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2 Preliminaries Requires Authentication Unlicensed Licensed Download PDF	18
3 The nonstationary ideal Requires Authentication Unlicensed Licensed Download PDF	48
4 The ℙmax-extension Requires Authentication Unlicensed Licensed Download PDF	115
5 Applications Requires Authentication Unlicensed Licensed Download PDF	184
6 ℙmax variations. 6.1 2ℙmax Requires Authentication Unlicensed Licensed Download PDF	291
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.1 ℚmax Requires Authentication Unlicensed Licensed Download PDF	310
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.2 ℚ*max Requires Authentication Unlicensed Licensed Download PDF	338
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.3 2ℚmax Requires Authentication Unlicensed Licensed Download PDF	374
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.4 Weak Kurepa trees and ℚmax Requires Authentication Unlicensed Licensed Download PDF	381
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.5 KTℚmax Requires Authentication Unlicensed Licensed Download PDF	388
6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.6 Null sets and the nonstationary ideal Requires Authentication Unlicensed Licensed Download PDF	409
6 ℙmax variations. 6.3 Nonregular ultrafilters on ω1 Requires Authentication Unlicensed Licensed Download PDF	427
7 Conditional variations Requires Authentication Unlicensed Licensed Download PDF	432
8 ♣ principles for ω1. 8.1 Condensation Principles Requires Authentication Unlicensed Licensed Download PDF	498
8 ♣ principles for ω1. 8.2 ℙ♣NSmax Requires Authentication Unlicensed Licensed Download PDF	507
8 ♣ principles for ω1. 8.3 The principles, ♣+NS and ♣++NS Requires Authentication Unlicensed Licensed Download PDF	585
9 Extensions of L(Γ, ℝ). 9.1 AD+ Requires Authentication Unlicensed Licensed Download PDF	617
9 Extensions of L(Γ, ℝ). 9.2 The ℙmax-extension of L(Γ, ℝ) Requires Authentication Unlicensed Licensed Download PDF	626
9 Extensions of L(Γ, ℝ). 9.3 The ℚmax-extension of L(Γ, ℝ) Requires Authentication Unlicensed Licensed Download PDF	646
9 Extensions of L(Γ, ℝ). 9.4 Chang’s Conjecture Requires Authentication Unlicensed Licensed Download PDF	649
9 Extensions of L(Γ, ℝ). 9.5 Weak and Strong Reflection Principles Requires Authentication Unlicensed Licensed Download PDF	664
9 Extensions of L(Γ, ℝ). 9.6 Strong Chang’s Conjecture Requires Authentication Unlicensed Licensed Download PDF	680
9 Extensions of L(Γ, ℝ). 9.7 Ideals on ω2 Requires Authentication Unlicensed Licensed Download PDF	697
10 Further results. 10.1 Forcing notions and large cardinals Requires Authentication Unlicensed Licensed Download PDF	769
10 Further results. 10.2 Coding into L(P(ω1)) Requires Authentication Unlicensed Licensed Download PDF	776
10 Further results. 10.3 Bounded forms of Martin’s Maximum Requires Authentication Unlicensed Licensed Download PDF	862
10 Further results. 10.4 Ω-logic Requires Authentication Unlicensed Licensed Download PDF	886
10 Further results. 10.5 Ω-logic and the Continuum Hypothesis Requires Authentication Unlicensed Licensed Download PDF	894
10 Further results. 10.6 The Axiom (*)+ Requires Authentication Unlicensed Licensed Download PDF	908
10 Further results. 10.7 The Effective Singular Cardinals Hypothesis Requires Authentication Unlicensed Licensed Download PDF	916
11 Questions Requires Authentication Unlicensed Licensed Download PDF	921
Bibliography Requires Authentication Unlicensed Licensed Download PDF	927
Index Requires Authentication Unlicensed Licensed Download PDF	931

Language: English
Publisher: De Gruyter
Edition: Reprint 2011
Pages
- Front matter: 6
- Main content: 934

eBook

Published: February 1, 2013
ISBN: 9783110804737