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1.

図書

図書
Paul C. Eklof, Alan H. Mekler
出版情報: Amsterdam : Elsevier, 2002  xxi, 597 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 65
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目次情報: 続きを見る
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:
2.

図書

図書
[by] Shwu-Yeng T. Lin [and] You-Feng Lin
出版情報: Boston : Houghton Mifflin, c1974  ix, 164 p ; 24 cm
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3.

図書

図書
K. Kuratowski and A. Mostowski ; translated from Polish by M. Mączyński
出版情報: Amsterdam : North-Holland , Warszawa : Polish Scientific Publishers, 1968  xi, 417 p ; 24 cm
シリーズ名: Studies in logic and the foundations of mathematics
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4.

図書

図書
Peter W. Zehna
出版情報: Boston : Allyn and Bacon, c1969  x, 193 p. ; 22 cm
シリーズ名: The Allyn and Bacon series : topics in contemporary mathematics
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5.

図書

図書
Cavaillès, Jean, 1903-1944
出版情報: Paris : Hermann, 1938  156 p ; 26 cm
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6.

図書

図書
András Hajnal, Peter Hamburger ; translated by Attila Máté
出版情報: Cambridge : Cambridge University Press, 1999  viii, 316 p. ; 23 cm
シリーズ名: London Mathematical Society student texts ; 48
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目次情報: 続きを見る
Preface
Introduction to set theory / Part I.:
Introduction
Notation, conventions / 1.:
Definition of equivalence. The concept of cardinality. The Axiom of Choice / 2.:
Countable cardinal, continuum cardinal / 3.:
Comparison of cardinals / 4.:
Operations with sets and cardinals / 5.:
Examples / 6.:
Ordered sets. Order types. Ordinals / 7.:
Properties of wellordered sets. Good sets. The ordinal operation / 8.:
Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem / 9.:
Definition of the cardinality operation. Properties of cardinalities. The cofinality operation / 10.:
Properties of the power operation / 11.:
Hints for solving problems marked with * in Part I
An axiomatic development of set theory / Appendix:
The Zermelo-Fraenkel axiom system of set theory / A1.:
Definition of concepts; extension of the language / A2.:
A sketch of the development. Metatheorems / A3.:
A sketch of the development. Definitions of simple operations and properties (continued) / A4.:
A sketch of the development. Basic theorems, the introduction of [omega] and R (continued) / A5.:
The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7 / A6.:
The role of the Axiom of Regularity / A7.:
Proofs of relative consistency. The method of interpretation / A8.:
Proofs of relative consistency. The method of models / A9.:
Topics in combinatorial set theory / Part II.:
Stationary sets / 12.:
[Delta]-systems / 13.:
Ramsey's Theorem and its generalizations. Partition calculus / 14.:
Inaccessible cardinals. Mahlo cardinals / 15.:
Measurable cardinals / 16.:
Real-valued measurable cardinals, saturated ideals / 17.:
Weakly compact and Ramsey cardinals / 18.:
Set mappings / 19.:
The square-bracket symbol. Strengthenings of the Ramsey counterexamples / 20.:
Properties of the power operation. Results on the singular cardinal problem / 21.:
Powers of singular cardinals. Shelah's Theorem / 22.:
Hints for solving problems of Part II
Bibliography
List of symbols
Name index
Subject index
Preface
Introduction to set theory / Part I.:
Introduction
7.

図書

図書
Paul J. Cohen
出版情報: New York ; Amsterdam : W.A. Benjamin, 1966  154 p. ; 24 cm
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8.

図書

図書
Per-Olov Löwdin and Quantum Theory Project, University of Florida
出版情報: New York : John Wiley & Sons, c1998  xi, 458 p. ; 25 cm
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9.

図書

図書
Krzysztof Ciesielski
出版情報: Cambridge : Cambridge University Press, 1997  xi, 236 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 39
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10.

図書

図書
Winfried Just, Martin Weese
出版情報: Providence, R.I. : American Mathematical Society, c1997  xiii, 224 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 18 . Discovering modern set theory ; 2
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目次情報: 続きを見る
Filters and ideals in partial orders
Trees A little Ramsey theory
The $\Delta$-system lemma Applications of the continuum hypothesis
From the Rasiowa-Sikorski lemma to Martin's
Axiom Martin's Axiom Hausdorff gaps
Closed unbounded sets and stationary sets
The $\diamond$-principle Measurable cardinals
Elementary submodels Boolean algebras
Appendix: Some general topology
Index
Index of symbols
Filters and ideals in partial orders
Trees A little Ramsey theory
The $\Delta$-system lemma Applications of the continuum hypothesis
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