Computable Structures and the Hyperarithmetical Hierarchy

Nonfiction, Science & Nature, Mathematics, Applied, Technology
Cover of the book Computable Structures and the Hyperarithmetical Hierarchy by C.J. Ash, J. Knight, Elsevier Science
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Author: C.J. Ash, J. Knight ISBN: 9780080529523
Publisher: Elsevier Science Publication: June 16, 2000
Imprint: Elsevier Science Language: English
Author: C.J. Ash, J. Knight
ISBN: 9780080529523
Publisher: Elsevier Science
Publication: June 16, 2000
Imprint: Elsevier Science
Language: English

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).

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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).

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