Working with the LR degrees

Working with the LR degrees

G. Barmpalias, A. Lewis and M. Soskova

Summary

We say that oracle A is LR reducible to oracle B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real , oracle B can also find patterns on the same real . 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.