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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Finitely generated codings and the degrees r.e. in a degree $ {\bf d}$


Author: Richard A. Shore
Journal: Proc. Amer. Math. Soc. 84 (1982), 256-263
MSC: Primary 03D25; Secondary 03D30
MathSciNet review: 637179
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Abstract: We introduce finitely generated (partial) lattices which can be used to code an arbitrary set $ D$. Results of Lerman, Shore and Soare are used to embed these lattices in the degrees r.e. in $ D$. Thus if the degrees r.e. in and above $ {\mathbf{d}}$ are isomorphic to those r.e. in and above $ {\mathbf{c}}$, $ {\mathbf{d}}$ and $ {\mathbf{c}}$ are of the same arithmetic degree. Similar applications are given to generic degrees and general homogeneity questions.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0637179-1
Keywords: Recursively enumerable degrees, homogeneity problems, generic degrees
Article copyright: © Copyright 1982 American Mathematical Society