2024/11/07 by Nicolas Chavarria, Chavarria, Nicolas
Mathematics · Engineering · #Functional Equations Stability Results #Stability and Controllability of Differential Equations #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2411.04903
We study ε-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for ε-stability and briefly discuss finitely satisfiable types. We then do a short survey of ε-stability in a theory. Finally, we consider the map that takes each formula to its "degree" of stability in a given theory and show that it is a seminorm. All of this is done in the context of a first-order formalism that allows predicates to take values in arbitrary compact metric spaces.