A presentation theorem for continuous logic and metric abstract elementary classes

摘要

In recent years, model theory has widened its scope to include metric structures by considering real-valued models whose underlying set is a complete metric space. We show that it is possible to carry out this work by giving presentation theorems that translate the two main frameworks (continuous first order logic and Metric Abstract Elementary Classes) into discrete settings (a nice fragment of L_(ω1,ω) and Abstract Elementary Classes, respectively). We also translate various notions of classification theory.