Abstract
The notion of cupping/noncupping has played an essential role in the study of various degree structures in the Ershov hierarchy. As an approach to refute Shoenfield conjecture, Yates (see [2]) proved the existence of a nonzero noncuppable r.e. degree, a degree cupping no incomplete r.e. degree to 0’. In contrast to this, Arslanov proved in [1] that nonzero noncuppable degrees do not exist in the structure of d.r.e. degrees, which shows that the structures of r.e. degrees and d.r.e. degrees are not elementary equivalent.
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Liu, J., Wu, G. (2010). Degrees with Almost Universal Cupping Property. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_30
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DOI: https://doi.org/10.1007/978-3-642-13962-8_30
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