Computable Structure Theory - Downey, Rodney G.

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Résumé :
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 ?11-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....

Biographie:
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Sommaire:
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: ·...