Automorphisms of the Lattice of Recursively Enumerable Sets (Memoirs of the American Mathematical Society)
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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.
Format:Paperback
Language:English
ISBN:0821826018
ISBN13:9780821826010
Release Date:March 1995
Publisher:Amer Mathematical Society
Length:151 Pages
Weight:0.65 lbs.
Dimensions:10.0" x 0.5" x 7.3"
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