Abstract
Downey and Lempp (J. Symbolic Logic 62 (1997) 1215–1240) have shown that the contiguous computably enumerable (c.e.) degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N 5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with local nonmodularity in the computably enumerable degrees.
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