Binary subtrees with few labeled paths

We prove several quantitative Ramseyan results involving ternary complete trees with {0, 1}-labeled edges where we attempt to find a complete binary subtree with as few labels as possible along its paths. One of these is used to answer a question of Simpson’s in computability theory; we show that there is a bounded Π0 1 class of positive measure which is not strongly (Medvedev) reducible to DNR3; in fact, the class of 1-random reals is not strongly reducible to DNR3.

• Type: Journal
• Year: 2011
• Where: COMBINATORICA
• Authors: Rodney G. Downey, Noam Greenberg, Carl G. Jockusch Jr., Kevin Milans
• Keywords: COMBINATORICA 2011, Medvedev, Optimization, Reals, Subtree