Effective metric structure theory / Johanna N.Y. Franklin, Isaac Goldbring, Timothy H. McNicholl.

Format:

Book

Author/Creator:

Franklin, Johanna N.Y., 1979-

Goldbring, Isaac, author.

McNicholl, Timothy H., author.

Series:

Springer monographs in mathematics 1439-7382

Springer monographs in mathematics, 1439-7382

Language:

English

Subjects (All):

Metric spaces.

Computable functions.

Recursion theory.

Algebra--Data processing.

Functional analysis.

Physical Description:

xiii, 164 pages : illustrations ; 25 cm.

Place of Publication:

Cham, Switzerland : Springer Nature Switzerland, [2026]

Summary:

"This monograph introduces the reader to the increasingly popular topic of computable metric structure theory, a subject which unifies methods from effective analysis and computable algebra into one coherent framework. Computable structure theory had been constrained to the algebraic and discrete realms, but in the past 10 years or so, much work has been done in extending this topic to structures from analysis such as metric spaces, Banach spaces, and operator algebras. This book is the first comprehensive treatment of these basic results and discusses several challenging open problems that have arisen. The book provides a foundation for the study of classic objects from functional analysis using tools from continuous model theory and computable structure theory. It is largely self contained, though it is assumed that the reader is familiar with first-order logic. It should prove useful to students and researchers in continuous logic looking to familiarize themselves with computable structure theory as well as to researchers in the latter field looking to extend their work to structures from analysis. The discussion contains a large number of well-crafted examples and could provide the basis for a course or seminar in this area." -- Provided by publisher.

Contents:

Introduction

An introduction to metric structures and their model theory

Framework for the computability of metric structures

Metric spaces

Banach spaces: C(X)-spaces

Banach spaces: LP spaces

Operator algebras

Degrees of theories

Appendix A: Collected open questions

Appendix B: Computability theory background.

Notes:

Includes bibliographical references and index.

ISBN:

9783032133212

3032133211

OCLC:

1591565153

Publisher Number:

CIPO000384656