Working with the LR Degrees

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.

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