Almost free modules : set-theoretic methods

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Almost free modules : set-theoretic methods / Paul C. Eklof, Alan H. Mekler

版:

Revised ed.

資料種別:

図書

出版情報:

Amsterdam : Elsevier, 2002

形態:

xxi, 597 p. ; 23 cm

シリーズ名:

North-Holland mathematical library ; v. 65 <BA00018746>

著者名:

ISBN:

9780444504920 [0444504923]

書誌ID:

BA57157800

子書誌情報

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Almost free modules : set-theoretic methods
Paul C. Eklof, Alan H. Mekler , North-Holland , 1990

書誌詳細

注記:

Includes bibliography and index

主題:

Abelian groups; Modules (Algebra); Set theory

言語:

英語

目次情報:

Algebraic Preliminaries / I：

Homomorphisms and extensions / 1：

Direct sums and products / 2：

Linear topologies / 3：

Set Theory / II：

Ordinary set theory

Filters and large cardinals

Ultraproducts

Clubs and stationary sets / 4：

Games and trees / 5：

utri;-systems and partitions / 6：

Slender Modules / III：

Introduction to slenderness

Examples of slender modules and rings

The Lstrok;os-Eda theorem

Almost Free Modules / IV：

Introduction to aleph; 1 free abelian groups / 0：

kgr;-free modules

aleph; 1 -free abelian groups

Compactness results

Pure Injective Modules / V：

Structure theory

Cotorsion groups

More Set Theory / VI：

Prediction Principles

Models of set theory

L, the constructible universe

MA and PFA

PCF theory and I [lgr;]

Almost Free Modules Revisisted (IV, VI) / VII：

aleph; 1 -free abelian groups revisited

kgr;-free modules revisited

kgr;-free abelian groups

Transversals, lgr;-systems and NPT

Reshuffling lgr;-systems / 3A：

Hereditarily separable groups

NPT and the construction of almost free groups

aleph; 1 -Separable Groups (VI, VII.0,1) / VIII：

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) / IX：

Perps and products

Countable products of the integers

Uncountable products of the integers

Radicals and large cardinals

Iterated Sums And Products (III) / X：

The Reid class

Types in the Reid class

Topological Methods (X, IV) / XI：

Inverse and direct limits

Completions

Density and dual bases

Groups of continuous functions

Sheaves of abelian groups

An Analysis Of Ext (VII, VIII.1) / XII：

Ext and Diamond

Ext, MA and Proper forcing

Baer modules

The structure of Ext

The structure of Ext when Hom=0

Uniformization (XII) / XIII：

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) / XIV：

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) / XV：

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) / XVI：

Orthogonal classes and splitters

Cotorsion theories

Almost free splitters

The Black Box and Ext

Dual Groups (IX, XI, XIV) / XVII：

Invariants of dual groups

Tree groups

Criteria for being a dual group

Some non-reflexive groups

Dual groups in L

Algebraic Preliminaries / I：

Homomorphisms and extensions / 1：

Direct sums and products / 2：

Linear topologies / 3：

Set Theory / II：

Ordinary set theory

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