A necessary and sufficient condition for embedding principally decomposable finite lattices into the computably enumerable degrees

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Abstract

We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.

MSC

Primary: 03D25

Keywords

Embedding
Computably enumerable set
Computably enumerable degree
Lattice

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Research supported by NSF grant DMS-9625445.