We study the groups Gal L and Gal KP, and the associated equivalence relations EL and EKP, attached to a first order theory T. An example is given where EL≠ EKP. It is proved that EKP is the composition of EL and the closure of EL. Other examples are given showing this is best possible.

Assume that the class of partial automorphisms of the monster model of a complete theory has the amalgamation property. The beautiful automorphisms are the automorphisms of models ofT which: 1. are strong, i.e. leave the algebraic closure (inT eq) of the empty set pointwise fixed, 2. are obtained by the Fraïsse construction using the amalgamation property that we have just mentioned. We show that all the beautiful automorphisms have the same theory (in the language ofT plus one unary function symbol (...) for the automorphism), and we study this theory. In particular, we examine the question of the saturation of the beautiful automorphisms. We also prove that in some cases (in particular if the theory is ω-stable andG-trivial), almost all (in the sense of Baire categoricity) automorphisms of the saturated countable model are beautiful and conjugate. (shrink)

We associate with every first order structure [Formula: see text] a family of invariant, locally Noetherian topologies. The structure is almost determined by the topologies, and properties of the structure are reflected by topological properties. We study these topologies in particular for stable structures. In nice cases, we get a behaviour similar to the Zariski topology in algebraically closed fields.

We give a characterisation of forking in the context of simple theories in terms of the fundamental order.

We give here alternative definitions for the notions that S. Shelah has introduced in recent papers: the dimensional order property and the depth of a theory. We will also give a proof that the depth of a countable theory, when defined, is an ordinal recursive in T.

Let M be a countable saturated structure, and assume that D(ν) is a strongly minimal formula (without parameter) such that M is the algebraic closure of D(M). We will prove the two following theorems: Theorem 1. If G is a subgroup of $\operatorname{Aut}(\mathfrak{M})$ of countable index, there exists a finite set A in M such that every A-strong automorphism is in G. Theorem 2. Assume that G is a normal subgroup of $\operatorname{Aut}(\mathfrak{M})$ containing an element g such that for all (...) n there exists $X \subseteq D(\mathfrak{M})$ such that $\operatorname{Dim}(g(X)/X) > n$. Then every strong automorphism is in G. (shrink)

The 1996 European Summer Meeting of the Association of Symbolic Logic was held held the University of the Basque Country, at Donostia (San Se bastian) Spain, on July 9-15, 1996. It was organised by the Institute for Logic, Cognition, Language and Information (ILCLI) and the Department of Logic and Philosophy of Sciences of the University of the Basque Coun try. It was supported by: the University of Pais Vasco/Euskal Herriko Unib ertsitatea, the Ministerio de Education y Ciencia (DGCYT), Hezkuntza Saila (...) (Eusko Jaurlaritza), Gipuzkoako Foru Aldundia, and Kuxta Fun dazioa. The main topics of the meeting were Model Theory, Proof Theory, Re cursion and Complexity Theory, Models of Arithmetic, Logic for Artifi cial Intelligence, Formal Semantics of Natural Language and Philosophy of Contemporary Logic. The Program Committee consisted of K. Ambos Spies (Heidelberg), J.L. Balcazar (Barcelona), J.E. Fenstad (Oslo), D. Israel (Stanford), H. Kamp (Stuttgart), R. Kaye (Birmingham), J.M. Larrazabal (San Sebastian), D. Lascar (Paris, chairman), A. Marcja (Firenze), G. Mints (Stanford), M. Otero (Madrid), S. Ronchi della Rocca (Torino), K. Segerberg (Uppsala) and L. Vega (Madrid). The organizing Committee consisted of X. Arrazola (San Sebastian), A. Arrieta (San Sebastian), R. Beneyeto (Valencia), B. Carrascal (San Se bastian), K. Korta (San Sebastian), J.M. Larrazabal (San Sebastian, chair man), J.C. Martinez (Barcelona), J.M. Mendez (Salamanca), F. Migura (Victoria) and J. Perez (Victoria). (shrink)