Around Superstability in Metric Abstract Elementary Classes

Abstract

En esta tesis estudiamos la unicidad de modelos límite como una noción débil de superestabilidad en clases elementales abstractas métricas, mostrando algunas consecuencias en el estudio de nociones de estabilidad geométrica como dominación, una noción débil de ortogonalidad y paralelismo, estudiando en algunos ejemplos los resultados obtenidos. Adicionalmente, estudiamos un teorema de transferencia de estabilidad bajo hipótesis de carácter local (superestabilidad) y docilidad. / Abstract. In this thesis, we study uniqueness of limit models as a weak version of superstability in metric abstract elementary classes, showing some consequences in some basic notions of geometric stability theory as domination, a weak notion of orthogonality and parallelism, studying the got results in some examples. Also, we study a stability transfer theorem under local character (superstability) and tameness in the setting of metric abstract elementary classes.

In this thesis, we study uniqueness of limit models as a weak version of superstability in metric abstract elementary classes, showing some consequences in some basic notions of geometric stability theory as domination, a weak notion of orthogonality and parallelism, studying the got results in some examples. Also, we study a stability transfer theorem under local character (superstability) and tameness in the setting of metric abstract elementary classes.