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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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Effective Lim Infs in Cantor Space
by
Peter Cholak
University of Notre Dame

Let Ui be subsets of Cantor Space. Then liminfUi = ∪m ∩n > m Un. We will explore effective versions the following classic result:

Let Ui be open sets of measure at most c in Cantor space, 2w, under the Lebesgue measure. Then liminfUi = ∪m ∩n > m Un has measure at most c. Then, for all e, there is a Ve that Ve has measure at most e+ c and Ve covers liminfUi.

This problem first arose in the paper, "Limit complexities revisited", by L. Bienvenu, A. Muchnik, A. Shen, and N. Vereshchagin.

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Date received: February 29, 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-16.