ENGLISH

Automorphisms of the Lattice of Recursively Enumerable Sets

By Peter Cholak

Book information

Publisher
American Mathematical Society
Year
1995
ISBN
0821826018, 9780821826010
Language
english
Format
PDF
Filesize
15 MB (16007404 bytes)
Series
Memoirs of the American Mathematical Society
Pages
151\168
Time added
2017-01-10 01:32:47
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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.

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