Computable Structure Theory

Within the Arithmetic

Antonio Montalbán (University of California, Berkeley)

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English

Cambridge University Press
24 June 2021

Mathematical logic; Set theory; Mathematical modelling

Series: Perspectives in Logic

In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.

By: Antonio Montalbán (University of California Berkeley)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 240mm, Width: 162mm, Spine: 18mm
Weight: 490g
ISBN: 9781108423298
ISBN 10: 1108423299
Series: Perspectives in Logic
Pages: 250
Publication Date: 24 June 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Structures; 2. Relations; 3. Existentially-Atomic Models; 4. Generic Presentations; 5. Degree Spectra; 6. Comparing Structures and Classes of Structures; 7. Finite-Injury Constructions; 8. Computable Categoricity; 9. The Jump of a Structure; 10. ∑-Small Classes; Bibliography; Index.

Antonio Montalbán is Professor of Mathematics at the University of California, Berkeley.

Reviews for Computable Structure Theory: Within the Arithmetic

'This exceptionally well-written book is the first modern monograph on computable structure theory in 20 years … The author succeeds in bringing together new and old results and presenting them in a coherent framework, making it easy for the reader to learn the main results and techniques in the area for application in their own research.' Alexandra Andreeva Soskova, MathSciNet