Metric Spaces Are Universal for Bi-interpretation with Metric Structures

  title={Metric Spaces Are Universal for Bi-interpretation with Metric Structures},
  author={James Hanson},
  journal={Annals of Pure and Applied Logic},
  • James Hanson
  • Published 27 March 2021
  • Mathematics, Computer Science
  • Annals of Pure and Applied Logic
3 Citations

Approximate Isomorphism of Metric Structures

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov and by Ben Yaacov, Berenstein, Henson, and Usvyatsov, which are

Analog reducibility

  • James Hanson
  • Mathematics, Computer Science
    J. Log. Comput.
  • 2021
In this paper we introduce and characterize two ‘analog reducibility’ notions for $[0,1]$-valued oracles on $\omega $ obtained by applying the syntactic characterizations of Turing and enumeration

Approximate Categoricity in Continuous Logic

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Point Degree Spectra of Represented Spaces

The point degree spectrum of a represented space is introduced as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on and creates a connection among various areas of mathematics including computability theory, descriptive set theory, infinite dimensional topology and Banach space theory.

Continuous first order logic for unbounded metric structures

We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than


We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable,

On d-finiteness in continuous structures

We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may


We develop continuous first order logic, a variant of the logic described by Chang and Keisler (1966). We show that this logic has the same power of expression as the framework of open Hausdorff

Computable Analysis: An Introduction

  • K. Weihrauch
  • Education
    Texts in Theoretical Computer Science. An EATCS Series
  • 2000
This book provides a solid fundament for studying various aspects of computability and complexity in analysis and is written in a style suitable for graduate-level and senior students in computer science and mathematics.

Model theory for metric structures, volume 2 of London Mathematical Society Lecture Note Series, pages 315–427

  • 2008

Model Theory. Encyclopedia of Mathematics and its Applications

  • 1993