We develop methods for coding with first-order formulas into the partial order E of enumerable sets under inclusion. First we use them to reprove and generalize the (unpublished) result of the first author that the elementary theory of E has the same computational complexity as the theory of the nat
β¦ LIBER β¦
Enumerating orientations of ordered sets
β Scribed by Wei-Ping Liu; Ivan Rival
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 488 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0012-365X
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## Abstract I introduce an effective enumeration of all effective enumerations of classes of r. e. sets and define with this the index set __IE__ of injectively enumerable classes. It is easy to see that this set is β~5~ in the Arithmetical Hierarchy and I describe a proof for the β~5~βhardness of