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Recursively Enumerable Sets and Degrees

Author: Robert I. Soare

Publisher: Springer Science & Business Media

Published: 1999-11-01

Total Pages: 460

ISBN-13: 9783540152996

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..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988

Book Synopsis Recursively Enumerable Sets and Degrees by : Robert I. Soare

Download or read book Recursively Enumerable Sets and Degrees written by Robert I. Soare and published by Springer Science & Business Media. This book was released on 1999-11-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: ..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988

递归可枚举集和图灵度/[英文本]/可计算函数与可计算生成集研究/国外数学名著系列/Recursively enumerable sets and degerees

Author: R.I.·索尔 (美)

Publisher:

Published: 1987

Total Pages: 437

ISBN-13: 9787030182951

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Book Synopsis 递归可枚举集和图灵度/[英文本]/可计算函数与可计算生成集研究/国外数学名著系列/Recursively enumerable sets and degerees by : R.I.·索尔 (美)

Download or read book 递归可枚举集和图灵度/[英文本]/可计算函数与可计算生成集研究/国外数学名著系列/Recursively enumerable sets and degerees written by R.I.·索尔 (美) and published by . This book was released on 1987 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Degree Theoretic Definitions on the Low2 Recursively Enumerable Sets

Author: Rod G. Downey

Publisher:

Published: 1992

Total Pages: 64

ISBN-13:

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Book Synopsis Degree Theoretic Definitions on the Low2 Recursively Enumerable Sets by : Rod G. Downey

Download or read book Degree Theoretic Definitions on the Low2 Recursively Enumerable Sets written by Rod G. Downey and published by . This book was released on 1992 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uniformity in the Recursively Enumerable Degrees and Infima in the Degrees of the Differences of Recursively Enumberable Sets

Author: Deborah Suzanne Kaddah

Publisher:

Published: 1992

Total Pages: 226

ISBN-13:

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Book Synopsis Uniformity in the Recursively Enumerable Degrees and Infima in the Degrees of the Differences of Recursively Enumberable Sets by : Deborah Suzanne Kaddah

Download or read book Uniformity in the Recursively Enumerable Degrees and Infima in the Degrees of the Differences of Recursively Enumberable Sets written by Deborah Suzanne Kaddah and published by . This book was released on 1992 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Turing and Truth Table Degrees of 1-generic and Recursively Enumerable Sets

Author: Christine Ann Haught

Publisher:

Published: 1985

Total Pages: 192

ISBN-13:

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Book Synopsis Turing and Truth Table Degrees of 1-generic and Recursively Enumerable Sets by : Christine Ann Haught

Download or read book Turing and Truth Table Degrees of 1-generic and Recursively Enumerable Sets written by Christine Ann Haught and published by . This book was released on 1985 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Automorphisms of the Lattice of Recursively Enumerable Sets

Author: Peter Cholak

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 166

ISBN-13: 0821826018

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A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.

Book Synopsis Automorphisms of the Lattice of Recursively Enumerable Sets by : Peter Cholak

Download or read book Automorphisms of the Lattice of Recursively Enumerable Sets written by Peter Cholak and published by American Mathematical Soc.. This book was released on 1995 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.

Degrees of Unsolvability

Author: Gerald E. Sacks

Publisher: Princeton University Press

Published: 1966

Total Pages: 192

ISBN-13: 9780691079417

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A classic treatment of degrees of unsolvability from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Book Synopsis Degrees of Unsolvability by : Gerald E. Sacks

Download or read book Degrees of Unsolvability written by Gerald E. Sacks and published by Princeton University Press. This book was released on 1966 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic treatment of degrees of unsolvability from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Computability in Analysis and Physics

Author: Marian B. Pour-El

Publisher: Cambridge University Press

Published: 2017-03-02

Total Pages: 219

ISBN-13: 1107168449

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The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.

Book Synopsis Computability in Analysis and Physics by : Marian B. Pour-El

Download or read book Computability in Analysis and Physics written by Marian B. Pour-El and published by Cambridge University Press. This book was released on 2017-03-02 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.

The Role of True Finiteness in the Admissible Recursively Enumerable Degrees

Author: Noam Greenberg

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 114

ISBN-13: 0821838857

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When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of $\alpha$-finiteness. As examples we discuss bothcodings of models of arithmetic into the recursively enumerable degrees, and non-distributive lattice embeddings into these degrees. We show that if an admissible ordinal $\alpha$ is effectively close to $\omega$ (where this closeness can be measured by size or by cofinality) then such constructions maybe performed in the $\alpha$-r.e. degrees, but otherwise they fail. The results of these constructions can be expressed in the first-order language of partially ordered sets, and so these results also show that there are natu

Book Synopsis The Role of True Finiteness in the Admissible Recursively Enumerable Degrees by : Noam Greenberg

Download or read book The Role of True Finiteness in the Admissible Recursively Enumerable Degrees written by Noam Greenberg and published by American Mathematical Soc.. This book was released on 2006 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: When attempting to generalize recursion theory to admissible ordinals, it may seem as if all classical priority constructions can be lifted to any admissible ordinal satisfying a sufficiently strong fragment of the replacement scheme. We show, however, that this is not always the case. In fact, there are some constructions which make an essential use of the notion of finiteness which cannot be replaced by the generalized notion of $\alpha$-finiteness. As examples we discuss bothcodings of models of arithmetic into the recursively enumerable degrees, and non-distributive lattice embeddings into these degrees. We show that if an admissible ordinal $\alpha$ is effectively close to $\omega$ (where this closeness can be measured by size or by cofinality) then such constructions maybe performed in the $\alpha$-r.e. degrees, but otherwise they fail. The results of these constructions can be expressed in the first-order language of partially ordered sets, and so these results also show that there are natu

Selected Logic Papers

Author: Gerald E Sacks

Publisher: World Scientific

Published: 1999-07-06

Total Pages: 452

ISBN-13: 9814496928

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The author selects 23 of his papers in mathematical logic that pursue definability via priority, forcing, compactness and fine structure applied to classical recursion, hyperarithmetic sets, recursion in objects of finite type, measure, models and E-recursion. His general introduction provides a chronology both personal and technical. Contents:On the Degrees Less Than 0'Recursive Enumerability and the Jump OperatorThe Recursively Enumerable Degrees are DenseA Simple Set Which is Not Effectively SimpleMetarecursive Sets (with G Kreisel)Post's Problem, Admissible Ordinals, and RegularityOn a Theorem of Lachlan and MartinA Minimal Hyperdegree (with R O Gandy)Measure-Theoretic Uniformity in Recursion Theory and Set TheoryRecursion in Objects of Finite TypeForcing with Perfect Closed SetsThe α-Finite Injury Method (with S G Simpson)The 1-Section of a Type n ObjectRemarks Against Foundational ActivityCountable Admissible Ordinals and HyperdegreesThe k-Section of a Type n ObjectEffective Bounds on Morley RankPost's Problem, Absoluteness and Recursion in Finite TypesOn the Number of Countable ModelsPost's Problem in E-RecursionThe Limits of E-Recursive EnumerabilityInadmissible Forcing (with T A Slaman)Effective Forcing Versus Proper Forcing Readership: Mathematical logicians and computer scientists. keywords:Recursion Theory;Computability Theory;Classical Degree Theory;Alpha-Recursion;E-Recursion;Model Theory;Splitting;Density;Jump "... this volume, together with Sacks' monograph on the subject, will be a useful source of information to those who want to bring life to the subject again." Mathematical Reviews

Book Synopsis Selected Logic Papers by : Gerald E Sacks

Download or read book Selected Logic Papers written by Gerald E Sacks and published by World Scientific. This book was released on 1999-07-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author selects 23 of his papers in mathematical logic that pursue definability via priority, forcing, compactness and fine structure applied to classical recursion, hyperarithmetic sets, recursion in objects of finite type, measure, models and E-recursion. His general introduction provides a chronology both personal and technical. Contents:On the Degrees Less Than 0'Recursive Enumerability and the Jump OperatorThe Recursively Enumerable Degrees are DenseA Simple Set Which is Not Effectively SimpleMetarecursive Sets (with G Kreisel)Post's Problem, Admissible Ordinals, and RegularityOn a Theorem of Lachlan and MartinA Minimal Hyperdegree (with R O Gandy)Measure-Theoretic Uniformity in Recursion Theory and Set TheoryRecursion in Objects of Finite TypeForcing with Perfect Closed SetsThe α-Finite Injury Method (with S G Simpson)The 1-Section of a Type n ObjectRemarks Against Foundational ActivityCountable Admissible Ordinals and HyperdegreesThe k-Section of a Type n ObjectEffective Bounds on Morley RankPost's Problem, Absoluteness and Recursion in Finite TypesOn the Number of Countable ModelsPost's Problem in E-RecursionThe Limits of E-Recursive EnumerabilityInadmissible Forcing (with T A Slaman)Effective Forcing Versus Proper Forcing Readership: Mathematical logicians and computer scientists. keywords:Recursion Theory;Computability Theory;Classical Degree Theory;Alpha-Recursion;E-Recursion;Model Theory;Splitting;Density;Jump "... this volume, together with Sacks' monograph on the subject, will be a useful source of information to those who want to bring life to the subject again." Mathematical Reviews