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.
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A coherent framework of results and techniques in computable structure theory, focusing on 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.
Antonio Montalbán is Professor of Mathematics at the University of California, Berkeley.
