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Automorphisms of the Lattice of Recursively Enumerable Sets
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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

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.

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