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Effective embeddings into strong degree structures

✍ Scribed by Timothy H. McNicholl

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 215 KB
Volume: 49
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310022

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✦ Synopsis

Abstract

We show that any partial order with a Σ~3~ enumeration can be effectively embedded into any partial order obtained by imposing a strong reducibility such as ≤~tt~ on the c. e. sets. As a consequence, we obtain that the partial orders that result from imposing a strong reducibility on the sets in a level of the Ershov hiearchy below ω + 1 are co‐embeddable.

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