Memoirs of the American Mathematical Society 1995; 151 pp; softcover Volume: 113 ISBN10: 0821826018 ISBN13: 9780821826010 List Price: US$46 Individual Members: US$27.60 Institutional Members: US$36.80 Order Code: MEMO/113/541
 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. Readership Mathematicians interested in recursion theory, mainly logicians and theoretical computer scientists. 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 Table of Contents  Introduction
 The extension theorem revisited
 The high extension theorems
 The proof of the high extension theorem I
 The proof of the high extension theorem II
 Lowness notions in the lattice of r.e. sets
 Bibliography
