By P. C. Eklof, A. H. Mekler
I. ALGEBRAIC PRELIMINARIES 1. Homomorphisms and extensions. 2. Direct sums and items. three. Linear topologies. II. SET idea 1. traditional set conception. 2. Filters and big cardinals. three. Ultraproducts. four. golf equipment and desk bound units. five. video games and timber. 6. u-systems and walls. III. slim MODULES 1.Introduction to slenderness. 2.Examples of slim modules and earrings. 3.The Los-Eda theorem. IV. virtually loose MODULES zero. creation to 1free abelian teams. 1. -free modules. 2. 1-free abelian teams. three. Compactness effects. V. natural INJECTIVE MODULES 1. constitution idea. 2. Cotorsion teams. VI. extra SET idea 1. Prediction rules. 2. versions of set thought. three. L, the constructible universe. four. MA and PFA. five. PCF concept and that i[ ]. VII. virtually loose MODULES REVISISTED (IV, VI) zero. 1-free abelian teams revisited. 1. -free modules revisited. 2. -free abelian teams. three. Transversals, -systems and NPT. 3A. Reshuffling -systems. four. Hereditarily separable teams. five. NPT and the development of just about loose teams. VIII. 1-SEPARABLE teams (VI, VII.0,1) 1. structures and definitions. 2. 1-separable teams lower than Martin's axiom. three. 1-separable teams below PFA. IX. QUOTIENTS of goods OF Z (III, IV, V) 1. Perps and items. 2. Countable items of the integers. three. Uncountable items of the integers. four. Radicals and big cardinals. X. ITERATED SUMS AND items (III) 1. The Reid type. 2. forms within the Reid classification. XI. TOPOLOGICAL tools (X, IV) 1. Inverse and direct limits. 2. Completions. three. Density and twin bases. four. teams of constant features. five. Sheaves of abelian teams. XII. AN research OF EXT (VII, VIII.1) 1. Ext and Diamond. 2. Ext, MA and correct forcing. three. Baer modules. four. The constitution of Ext. five. The constitution of Ext while Hom=0. XIII. UNIFORMIZATION (XII) zero. Whitehead teams and uniformization. 1. the elemental building and its purposes. 2. the need of uniformization. three. the variety of Whitehead teams. four. Monochromatic uniformization and hereditarily separable teams. XIV. THE BLACK field AND ENDOMORPHISM RINGS(V, VI) 1. Introducing the Black field. 2. evidence of the Black field. three. Endomorphism earrings of cotorsion-free teams. four. Endomorphism earrings of separable teams. five. vulnerable realizability of endomorphism jewelry and the Kaplansky try out difficulties. XV. a few buildings IN ZFC (VII, VIII, XIV) 1. A inflexible 1-free team of cardinality 1. 2. n-separable teams with the nook pathology. three. totally indecomposable modules. four. The lifestyles of -separable teams. XVI. COTORSION THEORIES, COVERS AND SPLITTERS(IX, XII.1, XIV) 1. Orthogonal sessions and splitters. 2. Cotorsion theories. three. virtually loose splitters. four. The Black field and Ext. XVII. twin teams (IX, XI, XIV) 1. Invariants of twin teams. 2. Tree teams. three. standards for being a twin crew. four. a few non-reflexive teams. five. twin teams in L
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Almost free modules. Set-theoretic methods by P. C. Eklof, A. H. Mekler