Automorphisms of the Lattice of Recursively Enumerable Sets (Memoirs of the American Mathematical Society) - Softcover

Cholak, Peter

 
9780821826010: Automorphisms of the Lattice of Recursively Enumerable Sets (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 0821826018 ISBN 13: 9780821826010
Verlag: American Mathematical Society, 1995

Inhaltsangabe

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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Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
American Mathematical Society
Erscheinungsdatum
1995
Sprache
Englisch
ISBN 10 
0821826018
ISBN 13 
9780821826010
Einband
Tapa blanda
Anzahl der Seiten
151
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