| eBook ISBN: | 978-1-4704-0120-7 |
| Product Code: | MEMO/113/541.E |
| List Price: | $46.00 |
| MAA Member Price: | $41.40 |
| AMS Member Price: | $27.60 |
| eBook ISBN: | 978-1-4704-0120-7 |
| Product Code: | MEMO/113/541.E |
| List Price: | $46.00 |
| MAA Member Price: | $41.40 |
| AMS Member Price: | $27.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 113; 1995; 151 ppMSC: Primary 03
This work explores the connection between the lattice of recursively enumerable (r.e.) sets and the r.e. Turing degrees. Cholak presents a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice. In addition to providing another proof of Soare's Extension Theorem, this technique is used to prove a collection of new results, including: every nonrecursive r.e. set is automorphic to a high r.e. set; and for every nonrecursive r.e. set \(A\) and for every high r.e. degree h there is an r.e. set \(B\) in h such that \(A\) and \(B\) form isomorphic principal filters in the lattice of r.e. sets.
ReadershipMathematicians interested in recursion theory, mainly logicians and theoretical computer scientists.
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Table of Contents
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Chapters
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I. Introduction
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II. The extension theorem revisited
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III. The high extension theorems
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IV. The proof of the high extension theorem I
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V. The proof of the high extension theorem II
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VI. Lowness notions in the lattice of r.e. sets
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Reviews
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Significant work ... clearly a must for workers in the area and for those looking towards studying amorphism groups of other related areas.
Journal of Symbolic Logic
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This work explores the connection between the lattice of recursively enumerable (r.e.) sets and the r.e. Turing degrees. Cholak presents a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice. In addition to providing another proof of Soare's Extension Theorem, this technique is used to prove a collection of new results, including: every nonrecursive r.e. set is automorphic to a high r.e. set; and for every nonrecursive r.e. set \(A\) and for every high r.e. degree h there is an r.e. set \(B\) in h such that \(A\) and \(B\) form isomorphic principal filters in the lattice of r.e. sets.
Mathematicians interested in recursion theory, mainly logicians and theoretical computer scientists.
-
Chapters
-
I. Introduction
-
II. The extension theorem revisited
-
III. The high extension theorems
-
IV. The proof of the high extension theorem I
-
V. The proof of the high extension theorem II
-
VI. Lowness notions in the lattice of r.e. sets
-
Significant work ... clearly a must for workers in the area and for those looking towards studying amorphism groups of other related areas.
Journal of Symbolic Logic
