It is consistent that there exists an ordered real closed field which is not hyper-real.
Krull-Gabriel dimension and Cantor-Bendixson rank of 1-domestic string algebras
We prove that the Krull-Gabriel dimension of the category of modules over any 1-domestic non-degenerate string algebra is 3.
La théorie d'un anneau de polynômes
Langages à valeurs réelles et applications
Le théorème de MacIntyre sur les ensembles définissables dans les corps -adiques
Les corps différentiellement clos dénombrables
Levelled O-minimal structures.
We introduce the notion of leveled structure and show that every structure elementarily equivalent to the real expo field expanded by all restricted analytic functions is leveled.
Limits of relatively hyperbolic groups and Lyndon’s completions
We describe finitely generated groups universally equivalent (with constants from in the language) to a given torsion-free relatively hyperbolic group with free abelian parabolics. It turns out that, as in the free group case, the group embeds into the Lyndon’s completion of the group , or, equivalently, embeds into a group obtained from by finitely many extensions of centralizers. Conversely, every subgroup of containing is universally equivalent to . Since finitely generated...
Linear and -linear betweenness spaces
Martin's Axiom Applied to Existentially Closed Groups.
m-normal theories
Originally, m-independence, ℳ -rank, m-stability and m-normality were defined only for small stable theories. Here we extend the definitions to an arbitrary small countable complete theory. Then we investigate these notions in the new, broader context. As a consequence we show that any superstable theory with countable models is m-normal. In particular, any *-algebraic group interpretable in such a theory is abelian-by-finite.
Model theoretic methods in the theory of topological fields.
Model theory of fields: An application to positive semidefinite polynomials
Model-completeness for sheaves of structures
Model-interpretability into trees and applications.
Models of second order arithmetic with definable Skolem functions
Non-axiomatizability of real spectra in
We show that the property of a spectral space, to be a spectral subspace of the real spectrum of a commutative ring, is not expressible in the infinitary first order language of its defining lattice. This generalises a result of Delzell and Madden which says that not every completely normal spectral space is a real spectrum.
Nota sobre una de las ecuaciones de Volterra de primera especie reducibles a ecuaciones de convolución.
Notes on exponential-logarithmic terms
On -categoricity and the theory of trees