Elementare Aussagen zur Arithmetik und Galoistheorie von Funktionenkörpern.
Elementary embeddings in torsion-free hyperbolic groups
We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if embeds elementarily in a torsion free hyperbolic group , we show that the group can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of with some free group and groups of closed surfaces. This gives as a corollary that an elementary subgroup of a finitely generated free group is a free factor. We also consider the...
Elementary equivalence and codimension in p-adic fields.
Elementary regular rings. II.
Embeddings into Simple Lattice-ordered Groups with Different First Order Theories.
End-extensions of countable structures and the induction schema
Endomorphisms of symbolic algebraic varieties
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...
Equational Reformulation Of Formal Theories
Errata to the paper "Models of second order arithmetic with definable Skolem functions", Fundamenta Mathematicae 75 (1972), pp. 223-234
Erratum to: “Elementary embeddings in torsion-free hyperbolic groups”
Existency-Closed Groups in X_1 with Special Properties
Exponentiations over the quantum algebra
We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra . We discuss two cases, according to whether the parameter is a root of unity. We show that the universal enveloping algebra of embeds in a non-principal ultraproduct of , where varies over the primitive roots of unity.
Extensions of Büchi's problem: Questions of decidability for addition and kth powers
We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...