| Edition |
1st ed. |
| Description |
1 online resource (xv, 346 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Studies in logic and the foundations of mathematics ; v. 144 |
|
Studies in logic and the foundations of mathematics ; v. 144.
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| Summary |
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). |
| Contents |
Preface. Computability. The arithmetical hierarchy. Languages and structures. Ordinals. The hyperarithmetical hierarchy. Infinitary formulas. Computable infinitary formulas. The Barwise-Kreisel Compactness Theorem. Existence of computable structures. Completeness and forcing. The Ash-Nerode Theorem. Computable categoricity and stability. <IT>n</IT>-systems. A-systems. Back-and forth relations. Theorems of Barker and Davey. Pairs of computable structures. Models of arithmetic. Special classes of structures. |
| Bibliography |
Includes bibliographical references (pages 323-333) and index. |
| Note |
Print version record. |
| Subject |
Computable functions.
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Fonctions calculables.
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MATHEMATICS -- Infinity.
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MATHEMATICS -- Logic.
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Computable functions
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Wiskundige logica.
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Fonctions calculables.
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Récursivité, Théorie de la.
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| Added Author |
Knight, J. (Julia)
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| Other Form: |
Print version: Ash, C.J. Computable structures and the hyperarithmetical hierarchy. 1st ed. Amsterdam ; New York : Elsevier, 2000 0444500723 9780444500724 (DLC) 00034103 (OCoLC)44046875 |
| ISBN |
9780444500724 |
|
0444500723 |
|
9780080529523 (electronic bk.) |
|
0080529526 (electronic bk.) |
| Standard No. |
AU@ 000048130997 |
|
CHNEW 001005950 |
|
DEBBG BV036962274 |
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DEBBG BV039830142 |
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DEBBG BV042317288 |
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DEBSZ 276857690 |
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DEBSZ 482353589 |
|
NZ1 12433121 |
|
NZ1 15192848 |
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AU@ 000075308723 |
|
