Computable Structures and the Hyperarithmetical Hierarchy

Elsevier (2000)
This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).
Keywords Computable functions
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Call number QA9.59.A84 2000
ISBN(s) 0444500723  
DOI 10.2307/2687759
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On Δ 2 0 -Categoricity of Equivalence Relations.Rod Downey, Alexander G. Melnikov & Keng Meng Ng - 2015 - Annals of Pure and Applied Logic 166 (9):851-880.
Indecomposable Linear Orderings and Hyperarithmetic Analysis.Antonio Montalbán - 2006 - Journal of Mathematical Logic 6 (01):89-120.

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