Undecidability and 1-types in intervals of the computably enumerable degrees

doi:10.1016/S0168-0072(99)00011-1

Annals of Pure and Applied Logic

Volume 106, Issues 1–3, 1 December 2000, Pages 1-47

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Abstract

We show that the theory of the partial ordering of the computably enumerable degrees in any given nontrivial interval is undecidable and has uncountably many 1-types.

MSC

03D25 (03C65 03D35 06A06)

Keywords

Computably enumerable degrees

Undecidability

One-types

Cited by (0)

¹: Partially supported by an Alfred P. Sloan Doctoral Dissertation Fellowship.

²: Partially supported by NSF Grants DMS-9503503 and DMS-9802843.