A hierarchy of Turing degrees : a transfinite hierarchy of lowness notions in the computably enumerable degrees, unifying classes, and natural definability / Rod Downey and Noam Greenberg.
Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields. This book introduces a new...
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| Online Access: |
Full Text (via University Press Scholarship Online) |
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| Main Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
Princeton :
Princeton University Press,
2021.
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| Series: | Annals of mathematics studies ;
number 206. Princeton scholarship online. |
| Subjects: |
| Summary: | Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications in topology, group theory, and other subfields. This book introduces a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. The book presents numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers. |
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| Item Description: | Previously issued in print: 2020. |
| Physical Description: | 1 online resource (240 pages) : illustrations (black and white) |
| Audience: | Specialized. |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9780691200217 (ebook) |
| DOI: | 10.23943/princeton/9780691199665.001.0001 |
| Source of Description, Etc. Note: | Description based on online resource; title from home page (viewed on December 17, 2020) |