arXiv subjects
Publications and source records attributed to Arturo Rodriguez Fanlo.
We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic notions such as compactness, positive closedness (existential closedness) and completeness (irreducibility).
We study type spaces and saturation for local positive logic.
The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence of Lie models. The second one is the stabilizer theorem. In the process, a systematic study of the structure of piecewise hyperdefinable sets is developed. In particular, we show the most significant properties of their logic topologies.
We prove that the group of automorphisms of the generic meet-tree expansion of an infinite non-unary free Fra\"ıssé limit over a finite relational language is simple. As a prototypical case, the group of automorphism of the Rado meet-tree (i.e. the Fra\"ıssé limit of finite graphs which are also meet-trees) is simple.