Embedding countable partial orderings in the enumeration degrees and the omega-enumeration degrees

作者：Soskova Mariya I^*; Soskov Ivan N

来源：Journal of Logic and Computation, 2012, 22(4): 927-952.

DOI：10.1093/logcom/exq051

• Enumeration degrees
• omega-enumeration degrees
• partial orderings
• iterated jumps
• good approximations

In this article, we examine the complexity of three degree structures in terms of the quantity of partial orderings embeddable in them. We prove that every countable partial ordering can be embedded in any interval of enumeration degrees with upper bound, a degree which contains a member with a good approximation. Next we prove that a similar result is true of the omega-enumeration degrees. Finally we consider the structure of the Sigma(2)(0) omega-enumeration degree modulo iterated jump and show that there as well one can embed densely every countable partial ordering.

• 出版日期2012-8