AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Automorphisms of the Lattice of Recursively Enumerable Sets
Peter Cholak
SEARCH THIS BOOK:

Memoirs of the American Mathematical Society
1995; 151 pp; softcover
Volume: 113
ISBN-10: 0-8218-2601-8
ISBN-13: 978-0-8218-2601-0
List Price: US$43
Individual Members: US$25.80
Institutional Members: US$34.40
Order Code: MEMO/113/541
[Add Item]

Request Permissions

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.

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
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia