Rodney G. Downey, Alexander Melnikov

Computable Structure Theory (eBook, PDF)

A Unified Approach

• Format: PDF

Produktbeschreibung

This is the first book which gives a unified theory for countable and uncountable computable structures.

The work treats computable linear orderings, graphs, groups and Boolean algebras unified with computable metric and Banach spaces, profinite groups, and the like. Further, it provides the first account of these that exploits effective versions of dualities, such as Stone and Pontryagin dualities. The themes are effective classification and enumeration.

Topics and features:

· · · · · Presents the first book treatment of Friedberg enumerations of structures

This unique volume is aimed at graduate students and researchers in computability theory, as well as mathematicians seeking to understand the algorithmic content of structure theory. Being self-contained, it provides ample opportunity for self-study.

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 540
• Erscheinungstermin: 21. August 2025
• Englisch
• ISBN-13: 9783031924330
• Artikelnr.: 75259794

Autorenporträt

Professor Rodney Downey and Associate Professor Alexander Melnikov both are affiliated with the School of Mathematics and Statistics at Victoria University, Wellington, New Zealand.

Inhaltsangabe

Part I Foundation of Computability.- 1. Introduction.- 2. Basics of Computability Theory.- 3. Computable Algebraic Structures.- 4. Computable Separable Spaces.- Part II Computable Duality.- 5. Computable Boolean Algebras.- 6. Computable Stone Spaces.- 7. Computable Abelian Groups.- 8. Computable Connected Compact Spaces.- Part III Computability and Classification Problems. 9. The Analytical Hierarchy and Sigma11-completeness.- 10. Computable Categoricity.- 11. Computable Banach Spaces with Applications.- 12. Resource Bounded Computation.- Part IV Non-computability and Randomness. 13. Randomness.- 14. Degree Spectra.- 15.- Computable Transfinite Analysis.