The limitations of cupping in the local structure of the enumeration degrees

Abstract We prove that a sequence of sets containing representatives of cupping partners for every nonzero 0 2 enumeration degree cannot have a 0 2 enumeration. We also prove that no subclass of the 0 2 enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to 0e by a single incomplete 0 2 enumeration degree. Keywords enumeration degrees, cupping, local structure, difference hierarchy Mathematics Subject Classification (2000) 03D30

• Type: Journal
• Year: 2010
• Where: AML
• Authors: Mariya Ivanova Soskova
• Keywords: AML 2010, Enumeration Degree, Local Structure, Nonzero