The infinite injury priority method

The Infinite Injury Priority Method

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Σ2 Induction and Infinite Injury Priority Arguments, Part Iii: Prompt Sets, Minimal Pairs and Shoenfield’s Conjecture

Priority constructions are the trademark of theorems on the recursively enumerable Turing degrees. By their combinatorial patterns, they are naturally identified as finite injury, infinite injury, and so forth. Following Chong and Yang [4], [3], we analyze the complexity of infinite injury arguments and pinpoint exactly the position of their degree-theoretic applications within the hierarchy of...

The Bounded Injury Priority Method and the Learnability of Unions of Rectangles

We develop a bounded version of the nite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain f0; : : :; n? 1g d with only equivalence queries. Applying this method, we show three main results: (1) The class of unions of rectangles is polynomial time learnable for constant dimension d. (2) The class of unions of rectangles who...

Injury research advocacy a high priority.

The Method of Infinite Descent in Stable

This paper is a continuation of [Rav02] and the second in a series of papers intended to clarify and expand results of the last chapter of [Rav04], in which we described a method for computing the Adams-Novikov E2-term and used it to determine the stable homotopy groups of spheres through dimension 108 for p = 3 and 999 for p = 5. The latter computation was a substantial improvement over prior ...