Computable Structure Theory
Beyond the Arithmetic

A coherent framework of results and techniques in computable structure theory, focusing on the hyperarithmetic and the infinitary languages.

Antonio Montalbán (Author)

9781108490252, Cambridge University Press

Hardback, published 19 February 2026

246 pages
23.4 x 15.6 x 1.6 cm, 0.54 kg

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.

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.

Subject Areas: Mathematical foundations [PBC]