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 massive cardinals. three. Ultraproducts. four. golf equipment and desk bound units. five. video games and bushes. 6. u-systems and walls. III. narrow MODULES 1.Introduction to slenderness. 2.Examples of slim modules and jewelry. 3.The Los-Eda theorem. IV. nearly unfastened MODULES zero. advent to 1free abelian teams. 1. -free modules. 2. 1-free abelian teams. three. Compactness effects. V. natural INJECTIVE MODULES 1. constitution thought. 2. Cotorsion teams. VI. extra SET idea 1. Prediction ideas. 2. types of set conception. three. L, the constructible universe. four. MA and PFA. five. PCF idea and that i[ ]. VII. nearly 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 unfastened teams. VIII. 1-SEPARABLE teams (VI, VII.0,1) 1. buildings and definitions. 2. 1-separable teams below Martin's axiom. three. 1-separable teams lower than 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 classification. 2. varieties within the Reid classification. XI. TOPOLOGICAL tools (X, IV) 1. Inverse and direct limits. 2. Completions. three. Density and twin bases. four. teams of continuing capabilities. 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 range 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. facts of the Black field. three. Endomorphism earrings of cotorsion-free teams. four. Endomorphism jewelry of separable teams. five. vulnerable realizability of endomorphism jewelry and the Kaplansky attempt difficulties. XV. a few buildings IN ZFC (VII, VIII, XIV) 1. A inflexible 1-free staff of cardinality 1. 2. n-separable teams with the nook pathology. three. completely indecomposable modules. four. The lifestyles of -separable teams. XVI. COTORSION THEORIES, COVERS AND SPLITTERS(IX, XII.1, XIV) 1. Orthogonal periods and splitters. 2. Cotorsion theories. three. nearly 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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