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

Berlin: de Gruyter, 2010. — 859 p.This is the revised and updated second edition of a well-established research monograph on the axiom of determinacy, written by an expert in the field. This axiom is a fundamental statement in set theory, and it is related to winning strategies in game theory.The nonstationary ideal on ω₁
The partial order P_{max}
P_{max} variations
Extensions of inner models beyond L(R)
Concluding remarks - the view from Berlin in 1999
The view from Heidelberg in 2010
Preliminaries
Weakly homogeneous trees and scales
Generic absoluteness
The stationary tower
Forcing Axioms
Refiection Principles
Generic ideals
The nonstationary ideal
The nonstationary ideal and δ¹₂
The nonstationary ideal and CH
The P_{max}-extension
Iterable structures
The partial order P_{max}
Applications
The sentence Φ_{AC}
Martin's Maximum and Φ_{AC}
The sentence Ψ_{AC}
The stationary tower and P_{max}
P*_{max}
P⁰_{max}232
The Axiom (^*_*)
Homogeneity properties of P(ω₁)/I_{NS}
P_{max} variations
²P_{max}
Variations for obtaining ω₁-dense ideals
Q_{max}
Q*_{max}
²Q_{max}
Weak Kurepa trees and Q_{max}
^{KT}Q_{max}
Null sets and the nonstationary ideal
Nonregular ultrafilters on ω₁
Conditional variations
Suslin trees
The Borel Conjecture
? principles for ω₁
Condensation Principles
P*^{NS}_{max}
the principles ?^+_[NS} and ?^{++}_{NS}
extensions of L(Γ,R)
AD+
The P_{max}-extension of L(Γ,R)
The basic analysis
Martin's Maximum ++(c)
The Q_{max}-extension of L(Γ,R)
Chang's Conjecture
Weak and Strong Refiection Principles
Strong Chang's Conjecture
Ideals on ω₂
Further results
Forcing notions and large cardinals
Coding into L(P(ω₁))
Coding by sets, ~S
Q^{(X)}_{max}
P^{(∅)}_{max}...(0,B)
P^{(∅,B)}_{max}
Bounded forms of Martin's Maximum
Ω-logic
Ω-logic and the Continuum Hypothesis
The Axiom (*)^+
The Effective Singular Cardinals Hypothesis
Questions