Computable Structure Theory
Beyond the Arithmetic
Will be published approx. on 31. January 2026
Book
Hardback
246 pages
978-1-108-49025-2 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 18 mm
Weight
540 gr
ISBN-13
978-1-108-49025-2 (9781108490252)
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Schweitzer Classification
Person
Antonio Montalban is Professor of Mathematics at the University of California, Berkeley.
Content
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.