Electronic ISBN:  9781470401207 
Product Code:  MEMO/113/541.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 

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 degreetheoretic 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.

Table of Contents

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


Reviews

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 degreetheoretic 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