Computable Structure Theory
Within the Arithmetic
Seiten
2021
Cambridge University Press (Verlag)
978-1-108-42329-8 (ISBN)
Cambridge University Press (Verlag)
978-1-108-42329-8 (ISBN)
Computable structure theory studies the relative complexity of mathematical structures. Written by a contemporary expert, this is the first full monograph on the subject in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings the main results and techniques in the field together into a coherent framework.
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.
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.
Antonio Montalbán is Professor of Mathematics at the University of California, Berkeley.
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.
| Erscheinungsdatum | 17.06.2021 |
|---|---|
| Reihe/Serie | Perspectives in Logic |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 162 x 240 mm |
| Gewicht | 490 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 1-108-42329-9 / 1108423299 |
| ISBN-13 | 978-1-108-42329-8 / 9781108423298 |
| Zustand | Neuware |
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