Almost Free Modules

Set-Theoretic Methods Volume 65

By: P. C. Eklof, A. H. Mekler

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Hardcover | 29 April 2002

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Hardcover
620 Pages

Edition Type
Revised

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22.86 x 15.88 x 3.18

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I. ALGEBRAIC PRELIMINARIES

1. Homomorphisms and extension s.

2. Direct sums and products.

3. Linear topologies.

II. SET THEORY

1. Ordinary set theory.

2. Filters and large cardinals.

3. Ultraproducts.

4. Clubs and stationary set s.

5. Games and trees.

6. ▵-systems a nd partitions.

III. SLENDER MODULES

1.Introduction to slenderness.

2.Examples of slende r modules and rings.

3.The Łoś-Eda theorem.

IV. ALMOST FREE MODULES

0. In troduction to ℵ1free abelian groups.

1. &kgr;-free modules.

2. ℵ1-free abelian g roups.

3. Compactness results.

V. PURE INJECTIVE MODULES

1. Structure theory.

2. Cotorsion groups.

VI. MO RE SET THEORY

1. Prediction Principles.

2.

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Algebraic Preliminaries
Homomorphisms and extensions
Direct sums and products
Linear topologies
Set Theory
Ordinary set theory
Filters and large cardinals
Ultraproducts
Clubs and stationary sets
Games and trees
utri;-systems and partitions
Slender Modules
Introduction to slenderness
Examples of slender modules and rings
The Lstrok;os-Eda theorem
Almost Free Modules
Introduction to aleph; 1 free abelian groups
kgr;-free modules
aleph; 1 -free abelian groups
Compactness results
Pure Injective Modules
Structure theory
Cotorsion groups
More Set Theory
Prediction Principles
Models of set theory
L, the constructible universe
MA and PFA
PCF theory and I [lgr;]
Almost Free Modules Revisisted (IV, VI)
aleph; 1 -free abelian groups revisited
kgr;-free modules revisited
kgr;-free abelian groups
Transversals, lgr;-systems and NPT
Reshuffling lgr;-systems
Hereditarily separable groups
NPT and the construction of almost free groups
aleph; 1 -Separable Groups (VI, VII.0,1)
Constructions and definitions
aleph; 1 -separable groups under Martin's axiom
aleph; 1 -separable groups under PFA
Quotients Of Products Of Z (III, IV, V)
Perps and products
Countable products of the integers
Uncountable products of the integers
Radicals and large cardinals
Iterated Sums And Products (III)
The Reid class
Types in the Reid class
Topological Methods (X, IV)
Inverse and direct limits
Completions
Density and dual bases
Groups of continuous functions
Sheaves of abelian groups
An Analysis Of Ext (VII, VIII.1)
Ext and Diamond
Ext, MA and Proper forcing
Baer modules
The structure of Ext
The structure of Ext when Hom=0
Uniformization (XII)
Whitehead groups and uniformization
The basic construction and its applications
The necessity of uniformization
The diversity of Whitehead groups
Monochromatic uniformization and hereditarily separable groups
The Black Box And Endomorphism Rings(V, VI)
Introducing the Black Box
Proof of the Black Box
Endomorphism rings of cotorsion-free groups
Endomorphism rings of separable groups
Weak realizability of endomorphism rings and the Kaplansky Test problems
Some Constructions In ZFC (VII, VIII, XIV)
A rigid aleph; 1 -free group of cardinality aleph; 1
aleph; n -separable groups with the Corner pathology
Absolutely indecomposable modules
The existence of lgr;-separable groups
Cotorsion Theories, Covers And Splitters(IX, XII.1, XIV)
Orthogonal classes and splitters
Cotorsion theories
Almost free splitters
The Black Box and Ext
Dual Groups (IX, XI, XIV)
Invariants of dual groups
Tree groups
Criteria for being a dual group
Some non-reflexive groups
Dual groups in L
Table of Contents provided by Publisher. All Rights Reserved.

Almost Free Modules

Set-Theoretic Methods Volume 65

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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