32 research outputs found
Continuous first order logic and local stability
We develop continuous first order logic, a variant of the logic described in
\cite{Chang-Keisler:ContinuousModelTheory}. We show that this logic has the
same power of expression as the framework of open Hausdorff cats, and as such
extends Henson's logic for Banach space structures. We conclude with the
development of local stability, for which this logic is particularly
well-suited
Generic separable metric structures
We compare three notions of genericity of separable metric structures. Our
analysis provides a general model theoretic technique of showing that
structures are generic in descriptive set theoretic (topological) sense and in
measure theoretic sense.
In particular, it gives a new perspective on Vershik's theorems on genericity
and randomness of Urysohn's space among separable metric spaces
Classification over a predicate -- the general case. Part I -- structure theory
We begin the development of structure theory for a first order theory stable
over a monadic predicate