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.
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This manuscript was prepared while the author was supported by NSF grant GJ-33168.
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Alton, D.A. Embedding relations in the lattice of recursively enumerable sets. Arch math Logik 17, 37–41 (1975). https://doi.org/10.1007/BF02280811
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DOI: https://doi.org/10.1007/BF02280811