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Definability via Kalimullin pairs in the structure of the enumeration degrees


Authors: Hristo A. Ganchev and Mariya I. Soskova
Journal: Trans. Amer. Math. Soc. 367 (2015), 4873-4893
MSC (2010): Primary 03D30
DOI: https://doi.org/10.1090/S0002-9947-2014-06157-6
Published electronically: November 24, 2014
MathSciNet review: 3335403
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Abstract: We give an alternative definition of the enumeration jump operator. We prove that the class of total enumeration degrees and the class of low enumeration degrees are first order definable in the local substructure of the enumeration degree, consisting of the elements bounded by $ {\mathbf {0}_e}'$.


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Additional Information

Hristo A. Ganchev
Affiliation: Faculty of Mathematics and Informatics, Sofia University, 1164 Sofia, Bulgaria
Email: ganchev@fmi.uni-sofia.bg

Mariya I. Soskova
Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94720
Address at time of publication: Faculty of Mathematics and Informatics, Sofia University, 1164 Sofia, Bulgaria
Email: msoskova@fmi.uni-sofia.bg

DOI: https://doi.org/10.1090/S0002-9947-2014-06157-6
Keywords: Enumeration reducibility, first order definability, enumeration jump, total enumeration degrees, low enumeration degrees
Received by editor(s): November 12, 2012
Received by editor(s) in revised form: April 10, 2013
Published electronically: November 24, 2014
Additional Notes: This research was supported by a BNSF grant No. DMU 03/07/12.12.2011 and by Sofia University SF grant No. 131/09.05.2012
The second author was supported by a Marie Curie international outgoing fellowship STRIDE (298471) within the 7th European Community Framework Programme and the Isaac Newton Institute for Mathematical Sciences in the programme ‘Semantics and Syntax’
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.