8,809 research outputs found
A presentation theorem for continuous logic and Metric Abstract Elementary Classes
We give a presentation theorem for continuous first-order logic and Metric
Abstract Elementary classes in terms of and Abstract
Elementary Classes, respectively. This presentation is accomplished by
analyzing dense subsets that are closed under functions. We extend this
correspondence to types and saturation
Modular functionals and perturbations of Nakano spaces
We settle several questions regarding the model theory of Nakano spaces left
open by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start by
studying isometric Banach lattice embeddings of Nakano spaces, showing that in
dimension two and above such embeddings have a particularly simple and rigid
form. We use this to show show that in the Banach lattice language the modular
functional is definable and that complete theories of atomless Nakano spaces
are model complete. We also show that up to arbitrarily small perturbations of
the exponent Nakano spaces are -categorical and -stable. In
particular they are stable
- …