Model theoretic stability and categoricity for complete metric spaces

Model Theoretic Stability and Categoricity for Complete Metric Spaces Sh837

We deal with systematic development of stability for the context of approximate elementary submodels of a monster metric space, which is not far, but still very different from first order model theory. In particular we prove the analogue of Morley’s theorem for classes of complete metric spaces.

Categoricity in homogeneous complete metric spaces

We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence of arbitrarily large models, joint embedding, amalgamation, homogeneity and a property which we call ...

Complete Metric Spaces

Complete Generalized Metric Spaces

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

On Generalized Complete Metric Spaces