Computable structure theory : within the arithmetic
著者
書誌事項
Computable structure theory : within the arithmetic
（Perspectives in logic）
Cambridge University Press , Association for Symbolic Logic, 2021
- : hardback
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注記
Includes bibliographical references (p. 177-186) and index
内容説明・目次
内容説明
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.
目次
- 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.
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