A decidable fragment of the elementary theory of the lattice of recursively enumerable sets

Lerman, M.; Soare, R. I.

doi:10.1090/S0002-9947-1980-0549153-7

A decidable fragment of the elementary theory of the lattice of recursively enumerable sets
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by M. Lerman and R. I. Soare

Trans. Amer. Math. Soc. 257 (1980), 1-37

DOI: https://doi.org/10.1090/S0002-9947-1980-0549153-7

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Abstract:

A natural class of sentences about the lattice of recursively enumerable sets modulo finite sets is shown to be decidable. This class properly contains the class of sentences previously shown to be decidable by Lachlan. New structure results about the lattice of recursively enumerable sets are proved which play an important role in the decision procedure.

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