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

作者：Soskova Mariya I^*

来源：Archive for Mathematical Logic, 2010, 49(2): 169-193.

DOI：10.1007/s00153-009-0171-1

• Enumeration degrees
• Cupping
• Local structure
• Difference hierarchy

We prove that a sequence of sets containing representatives of cupping partners for every nonzero Delta(0)(2) enumeration degree cannot have Delta(0)(2) enumeration. We also prove that no subclass of the Sigma(0)(2) enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to 0(e)' by a single incomplete Sigma(0)(2) enumeration degree.

• 出版日期2010-3