Automorphisms of the lattice of recursively enumerable sets
Author(s)
Bibliographic Information
Automorphisms of the lattice of recursively enumerable sets
（Memoirs of the American Mathematical Society, no. 541）
American Mathematical Society, 1995
Available at / 19 libraries
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliography (p. 149-150)
"January 1995, volume 113, number 541 (first of 4 numbers)"
Description and Table of Contents
Description
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 non recursive r.e. set is automorphic to a high r.e. set; and for every non recursive 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.
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.
by "Nielsen BookData"
