# ON THE LATTICE OF RECURSIVELY ENUMERABLE SETS

@article{Lachlan1968ONTL, title={ON THE LATTICE OF RECURSIVELY ENUMERABLE SETS}, author={Alistair H. Lachlan}, journal={Transactions of the American Mathematical Society}, year={1968}, volume={130}, pages={1-37} }

This paper presents some new theorems concerning recursively enumerable (r.e.) sets. The aim of the paper is to advance the search for a decision procedure for the elementary theory of r.e. sets. More precisely, an effective method is sought for deciding whether or not an arbitrary sentence formulated in the lower predicate calculus with sole relative symbol c is true of the r.e. sets. The main achievement of the paper is the characterisation of the hh-simple sets as those coinfinite r.e. sets…

## 156 Citations

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- 1971

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