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Embedding relations in the lattice of recursively enumerable sets

Embedding relations in the lattice of recursively enumerable sets Let ℰ* be the lattice of recursively enumerable sets of natural numbers modulo finite differences. We characterize the relations which can be embedded in ℰ* by using certain collections of maximal sets as domain and using Lachlan's notion of major subsets to code in the relation in certain natural ways. We show that attempts to prove the undecidability of ℰ* by using such embeddings fail. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Embedding relations in the lattice of recursively enumerable sets

Alton, Donald
Archive for Mathematical Logic , Volume 17 (2) – Nov 27, 2005
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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1975 by Verlag W. Kohlhammer
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/BF02280811
Publisher site
See Article on Publisher Site

Abstract

Let ℰ* be the lattice of recursively enumerable sets of natural numbers modulo finite differences. We characterize the relations which can be embedded in ℰ* by using certain collections of maximal sets as domain and using Lachlan's notion of major subsets to code in the relation in certain natural ways. We show that attempts to prove the undecidability of ℰ* by using such embeddings fail.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Nov 27, 2005

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