Degree spectra and immunity properties

Mathematical Logic Quarterly 56 (1):67-77 (2010)
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Abstract

We analyze the degree spectra of structures in which different types of immunity conditions are encoded. In particular, we give an example of a structure whose degree spectrum coincides with the hyperimmune degrees. As a corollary, this shows the existence of an almost computable structure of which the complement of the degree spectrum is uncountable

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Citations of this work

Relative to any non-hyperarithmetic set.Noam Greenberg, Antonio Montalbán & Theodore A. Slaman - 2013 - Journal of Mathematical Logic 13 (1):1250007.
The degrees of bi-hyperhyperimmune sets.Uri Andrews, Peter Gerdes & Joseph S. Miller - 2014 - Annals of Pure and Applied Logic 165 (3):803-811.
Spectra of Atomic Theories.Uri Andrews & Julia F. Knight - 2009 - Journal of Symbolic Logic 78 (4):1189-1198.

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References found in this work

Degrees coded in jumps of orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
The degrees of bi‐immune sets.Carl G. Jockusch - 1969 - Mathematical Logic Quarterly 15 (7‐12):135-140.
Notions of weak genericity.Stuart A. Kurtz - 1983 - Journal of Symbolic Logic 48 (3):764-770.
The degrees of bi-immune sets.Carl G. Jockusch - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (7-12):135-140.

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