Abstract
We say that A ≤ LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ, oracle B can also find patterns on γ. In other words, B is at least as good as A for this purpose. We propose a methodology for studying the LR degrees and present a number of recent results of ours, including sketches of their proofs.
Barmpalias was supported by EPSRC Research Grant No. EP/C001389/1 and would also like to thank Steve Simpson for a number of stimulating discussions, as well as Doug Cenzer for his hospitality during a visit to the University of Florida, September-November 2006. Lewis was supported by Marie-Curie Fellowship No. MEIF-CT-2005-023657. Soskova was supported by the Marie Curie Early Training grant MATHLOGAPS (MEST-CT-2004-504029). All authors were partially supported by the NSFC Grand International Joint Project, No. 60310213, New Directions in the Theory and Applications of Models of Computation.
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Barmpalias, G., Lewis, A.E.M., Soskova, M. (2007). Working with the LR Degrees. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_8
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