Automorphisms of the lattice of recursively enumerable sets / Peter Cholak.

Format:

Book

Author/Creator:

Cholak, Peter, 1962- author.

Series:

Memoirs of the American Mathematical Society ; Number 541.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 541

Language:

English

Subjects (All):

Recursively enumerable sets.

Automorphisms.

Lattice theory.

Physical Description:

1 online resource (166 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1995.

Language Note:

English

Summary:

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.

Contents:

""Table of Contents""; ""Chapter I: Introduction""; ""Chapter II: The Extension Theorem Revisited""; ""Chapter III: The High Extension Theorems""; ""Chapter IV: The Proof of the High Extension Theorem I""; ""Chapter V: The Proof of the High Extension Theorem II""; ""Chapter VI: Lowness Notions in the Lattice of R.E. Sets""; ""Bibliography""

Notes:

"January 1995, Volume 113, Number 541 (first of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0120-7