Title Computable structure theory : within the arithmetic / Antonio Mantalbán

Published Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press ; Ithaca, NY : Association for Symbolic Logic, 2021

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Description 1 online resource (xxii, 190 pages) Series Perspectives in logic Perspectives in logic. Contents Cover -- Half-title -- Series information -- Title page -- Copyright information -- Dedication -- CONTENTS -- PREFACE -- NOTATION AND CONVENTIONS -- Chapter 1 STRUCTURES -- 1.1. Presentations -- 1.2. Presentations that code sets -- Chapter 2 RELATIONS -- 2.1. Relatively intrinsic notions -- 2.2. Complete relations -- 2.3. Examples of r.i.c.e. complete relations -- 2.4. Superstructures -- Chapter 3 EXISTENTIALLY-ATOMIC MODELS -- 3.1. Definition -- 3.2. Existentially algebraic structures -- 3.3. Cantor's back-and-forth argument -- 3.4. Uniform computable categoricity -- 3.5. Existential atomicity in terms of types -- 3.6. Building structures and omitting types -- 3.7. Scott sentences of existentially atomic structures -- 3.8. Turing degree and enumeration degree -- Chapter 4 GENERIC PRESENTATIONS -- 4.1. Cohen generic reals -- 4.2. Generic enumerations of sets -- 4.3. Generic enumerations of structures -- 4.4. Relations on generic presentations -- Chapter 5 DEGREE SPECTRA -- 5.1. The c.e. embeddability condition -- 5.2. Co-spectra -- 5.3. Degree spectra that are not possible -- 5.4. Some particular degree spectra -- Chapter 6 COMPARING STRUCTURES AND CLASSES OF STRUCTURES -- 6.1. Muchnik and Medvedev reducibilities -- 6.2. Turing-computable embeddings -- 6.3. Computable functors and effective interpretability -- 6.4. Reducible via effective bi-interpretability -- Chapter 7 FINITE-INJURY CONSTRUCTIONS -- 7.1. Priority constructions -- 7.2. The method of true stages -- 7.3. Approximating the settling-time function -- 7.4. A construction of linear orderings -- Chapter 8 COMPUTABLE CATEGORICITY -- 8.1. The basics -- 8.2. Relative computable categoricity -- 8.3. Categoricity on a cone -- 8.4. When relative and plain computable categoricity coincide -- 8.5. When relative and plain computable categoricity diverge -- Chapter 9 THE JUMP OF A STRUCTURE Summary Presents main results and techniques in computable structure theory together in a coherent framework for the first time in 20 years Bibliography Includes bibliographical references and index Notes Online resource; title from digital title page (viewed on June 29, 2021) Subject Computable functions. Funciones computables Computable functions Form Electronic book ISBN 9781108525749 1108525741

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