Set Theory: The Third Millennium Edition, revised and expanded

Portada
Springer Science & Business Media, 23 de maig 2007 - 772 pàgines

Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.

 

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Continguts

Axioms of Set Theory
3
Ordinal Numbers 17
16
Cardinality Alephs The Canonical WellOrdering of α α Cofinality
35
The Axiom of Regularity
63
Stationary Sets
91
Combinatorial Set Theory 107
106
Partition Properties Weakly Compact Cardinals Trees Almost Disjoint Sets
125
Borel and Analytic Sets
139
Very Large Cardinals
365
Large Cardinals and Forcing 389
388
Saturated Ideals
409
The Nonstationary Ideal 441
440
The Singular Cardinal Problem
457
Descriptive Set Theory
479
The Real Line 511
510
Combinatorial Principles in L 545
543

Borel Sets Analytic Sets The Suslin Operation A The Hierarchy of Projective
154
Constructible Sets
175
The Hierarchy of Constructible Sets Gödel Operations Inner Models of
199
Forcing Conditions and Generic Sets Separative Quotients and Complete
225
Iterated Forcing and Martins Axiom 267
266
Large Cardinals
285
Large Cardinals and L 311
310
Silver Indiscernibles Models with Indiscernibles Proof of Silvers Theorem
337
A Nonconstructible 13 Real Namba Forcing A Cohen Real Adds a Suslin
573
Proper Forcing
601
More Descriptive Set Theory
615
Supercompact Cardinals and the Real Line 647
646
Forcing and Large Cardinals
669
More on Stationary Sets
695
Notation
733
Copyright

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