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Conference on Computability, Complexity and Randomness
May 19-23, 2008
Institute of Mathematical Science, Nanjing University.
Nanjing, JiangSu Province, P. R. of China

Organizers
Verónica Becher (University of Buenos Aires, Argentina), Rod Downey (Victoria University, Wellington, New Zealand), Denis Hirschfeldt (University of Chicago, USA), Jack Lutz (Iowa State University, USA), Wolfgang Merkle (Universität Heidelberg, Germany), Joseph Miller (University of Connecticut, USA), Liang Yu (Nanjing University, China)

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A promptly simple set which is not superlow cuppable
by
David Diamondstone
University of Chicago

A classical theorem in computability is that every promptly simple set can be cupped in the Turing degrees to some complete set by a low c.e. set. A related question due to A. Nies is whether every promptly simple set can be cupped by a superlow c.e. set, i.e. one whose Turing jump is truth-table reducible to the halting problem ∅'. A negative answer to this question is provided by giving an explicit construction of a promptly simple set which is not superlow cuppable. This relates to various other notions of lowness, randomness, and elementary definability in the c.e. degrees.

Date received: May 6, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawo-28.