Groups and Model Theory.

Intro -- About the conference -- A few words about R"udiger -- Chapter 1. -- Functorial properties of Hom and Ext -- 1. Introduction -- 2. Functors Acting on Sums and Products -- 3. Hom and Ext -- 4. -small groups -- 5. -extendible groups -- References -- Rigid abelian groups and the probabilistic method -- 1. Introduction -- 2. The probabilistic method: A brief introduction -- 3. Groups via -adic numbers -- 4. Small-rank groups -- 5. Concluding remarks and open questions -- 6. Acknowledgments -- References -- On projection-invariant subgroups of Abelian -groups -- 1. Introduction -- 2. Direct Powers -- References -- Looking for indecomposable right bounded complexes -- Introduction -- 1. Preliminaries -- 2. Examples -- References -- Butler's theorem revisited -- Introduction -- 1. Notation and basic settings -- 2. Regularity -- 3. Previous results -- 4. The (1) case -- 5. The (2) case -- 6. The general case -- 7. The concrete solution -- 8. Cancelling Primes -- 9. Realizing the converse of Butler's Theorem -- References -- The role of the Jacobson radical in isomorphism theorems -- 1. Introduction -- 2. Preliminaries -- 3. Determining the Torsion -- 4. Rank One Mixed Modules -- 5. Warfield Modules -- References -- Dimension in topological structures: Topological closure and local property -- 1. Introduction -- 2. Closure -- 3. Local property -- 4. Some examples -- References -- On kernel modules of cotorsion pairs -- 1. Introduction -- 2. Modules in the kernel -- 3. Applications to almost perfect domains -- 4. Weak-injective envelopes -- 5. Flat covers -- References -- Absolutely rigid fields and Shelah's absolutely rigid trees -- 1. Introduction -- 2. Absolutely rigid fields -- 3. Absolutely rigid trees -- References -- A note on Hopfian and co-Hopfian abelian groups -- 1. Introduction.

2. Lifting Hopficity (co-Hopficity) from Subgroups -- 3. Mixed groups -- References -- Upper cardinal bounds for absolute structures -- 1. Introduction -- 2. Partition Principles -- 3. The Erdös Cardinal ( ) and Trees -- 4. Constructing Absolutely Rigid Families of Trees -- 5. Nash-Williams Theory of Coloured Trees -- 6. Countable groups with large endomorphism rings -- References -- Undefinability of local Warfield groups in _{∞ } -- 1. Introduction -- 2. Background -- 3. Definability -- 4. Undefinability -- 5. Conclusions -- References -- Abelian groups with partial decomposition bases in _{∞ }^{ }, Part I -- 1. Introduction -- 2. Notations and terminology -- 3. Model-theoretic preliminaries -- 4. Equivalence in _{∞ } -- 5. Equivalence in ^{ }_{∞ }: Local classification -- 6. Equivalence in ^{ }_{∞ }: Global classification -- References -- Abelian groups with partial decomposition bases in _{∞ }^{ }, Part II -- 1. Introduction -- 2. Algebraic background -- 3. Model theory background -- 4. The classification theorem -- References -- Automorphism towers and automorphism groups of fields without Choice -- 1. Introduction and preliminaries -- 2. A variant of _{| |}^{ } and some corollaries of Main Theorem A -- 3. Coding structures as graphs -- 4. Some group theory -- 5. Proof of Main Theorem A from Main Theorem B -- 6. Coding graphs as fields -- References -- On subgroups of totally projective primary abelian groups and direct sums of cyclic groups -- 1. Terminology and introduction -- 2. A new characterization of C-decomposability -- 3. Weak ^{ ⋅2}-Projective Groups -- References -- Generic endomorphisms of homogeneous structures -- 1. Introduction -- 2. General conditions for the existence of generics -- 3. The trivial structure -- 4. The ordered rationals -- 5. The random graph -- 6. Other structures -- References.

Special pairs and automorphisms of centreless groups -- 1. Introduction -- 2. Automorphism towers -- 3. Unique Polish group topologies -- 4. An absoluteness result for automorphism towers of countable centreless groups -- 5. Groups of autohomeomorphism -- 6. Special pairs that are not strongly special -- References -- Pseudofinite groups with NIP theory and definability in finite simple groups -- 1. Introduction -- 2. Proof of Theorem 1.1 -- 3. A pseudofinite NIP group which is not soluble-by-finite -- 4. Model theory of finite simple groups -- References -- (1,2)-groups for a regulator quotient of exponent ⁴ -- 1. Introduction -- 2. Coordinate Matrices -- 3. Some matrix results -- 4. Direct Decomposition and Coordinate Matrices -- 5. Indecomposable (1,2)-Groups -- References -- On the macro structure of torsion free groups -- 1. Introduction -- 2. Some Generalities -- 3. Some special groups -- 4. Endomorphisms -- 5. Applications -- References -- Some results on the algebraic entropy -- 1. Introduction -- 2. On the Uniqueness of the -Entropy -- 3. Algebraic vs Topological Isomorphisms between Endomorphism Rings -- 4. Endomorphism rings of -groups with different algebraic entropy supports -- References -- Modules and Infinitary Logics -- 0. Introduction -- 1. Preliminaries -- 2. Eliminating quantifiers -- 3. Stability -- 4. How much does the subgroup exhaust a group -- 5. Concluding Remark -- References.

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