Computable Structure Theory: Beyond the Arithmetic
Author:   Antonio Montalbán (University of California, Berkeley)
Publisher:   Cambridge University Press
ISBN:  

9781108490252


Pages:   246
Publication Date:   19 February 2026
Format:   Hardback
Availability:   Not yet available, will be POD   Availability explained
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Computable Structure Theory: Beyond the Arithmetic


Overview

Computable structure theory quantifies and studies the relative complexity of mathematical structures. This text, in conjunction with the author's previous volume, represents the first full monograph on computable structure theory in two decades. 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. Geared towards graduate students and researchers in mathematical logic, the book enables the reader to learn all the main results and techniques in the area for application in their own research. While the previous volume focused on countable structures whose complexity can be measured within arithmetic, this second volume delves into structures beyond arithmetic, moving into the realm of the hyperarithmetic and the infinitary languages.

Full Product Details

Author:   Antonio Montalbán (University of California, Berkeley)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Weight:   0.500kg
ISBN:  

9781108490252


ISBN 10:   1108490255
Pages:   246
Publication Date:   19 February 2026
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Forthcoming
Availability:   Not yet available, will be POD   Availability explained
This item is yet to be released. You can pre-order this item and we will dispatch it to you upon it's release. This is a print on demand item which is still yet to be released.

Table of Contents

Notation and conventions from computability theory; Notation and conventions from Part I: 1. Ordinals; 2. Infinitary logic; 3. Computably infinitary languages; 4. Pi-one-one sets; 5. Hyperarithmetic sets; 6. Overspill; 7. Forcing; 8. The game metatheorem; 9. Iterated true-stage arguments; 10. Iterating the jump of a structure; 11. The isomorphism problem; 12. Vaught's conjecture; Bibliography; Index.

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Author Information

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

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