Ordinal Definability and Recursion Theory: Volume 3

Ordinal Definability and Recursion Theory: Volume 3 PDF

Author: Alexander S. Kechris

Publisher: Cambridge University Press

Published: 2016-01-11

Total Pages: 552

ISBN-13: 1316586286

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The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

The Cabal Seminar

The Cabal Seminar PDF

Author: Alexander S. Kechris

Publisher:

Published: 2016

Total Pages: 552

ISBN-13: 9781316588086

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The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

Recursion Theory

Recursion Theory PDF

Author: Chi Tat Chong

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-08-17

Total Pages: 322

ISBN-13: 3110275643

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This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.

Higher Recursion Theory

Higher Recursion Theory PDF

Author: Gerald E. Sacks

Publisher: Cambridge University Press

Published: 2017-03-02

Total Pages: 361

ISBN-13: 1107168430

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This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.

Definability and Computability

Definability and Computability PDF

Author: I︠U︡riĭ Leonidovich Ershov

Publisher: Springer Science & Business Media

Published: 1996-04-30

Total Pages: 288

ISBN-13: 9780306110399

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In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Gödel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.

Selected Logic Papers

Selected Logic Papers PDF

Author: Gerald E. Sacks

Publisher: World Scientific

Published: 1999

Total Pages: 460

ISBN-13: 9789810232672

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Contents: Recursive Enumerability and the Jump Operator; On the Degrees Less Than 0'; A Simple Set Which Is Not Effectively Simple; The Recursively Enumerable Degrees Are Dense; Metarecursive Sets (with G Kreisel); Post's Problem, Admissible Ordinals and Regularity; On a Theorem of Lachlan and Marlin; A Minimal Hyperdegree (with R O Gandy); Measure-Theoretic Uniformity in Recursion Theory and Set Theory; Forcing with Perfect Closed Sets; Recursion in Objects of Finite Type; The a-Finite Injury Method (with S G Simpson); Remarks Against Foundational Activity; Countable Admissible Ordinals and Hyperdegrees; The 1-Section of a Type n Object; The k-Section of a Type n Object; Post's Problem, Absoluteness and Recursion in Finite Types; Effective Bounds on Morley Rank; On the Number of Countable Models; Post's Problem in E-Recursion; The Limits of E-Recursive Enumerability; Effective Versus Proper Forcing.

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