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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
ISBN-13
978-0-8218-2601-0 (9780821826010)
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Schweitzer Klassifikation
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.
