16 citations · 18 across the 4 of their papers we have counts for
7 papers
Cousin's lemma in second-order arithmetic
Jordan Mitchell Barrett, Rodney G. Downey, Noam Greenberg
Cousin's lemma is a compactness principle that naturally arises when studying the gauge integral, a generalisation of the Lebesgue integral. We study the axiomatic strength of Cous…
Realizing Computably Enumerable Degrees in Separating Classes
Peter Cholak, Rod Downey, Noam Greenberg +1
We investigate what collections of c.e.\ Turing degrees can be realised as the collection of elements of a separating class of c.e.\ degree. We show that for every c.e.\ de…
Three topological reducibilities for discontinuous functions
Adam R. Day, Rod Downey, Linda Brown Westrick
We define a family of three related reducibilities, , and , for arbitrary functions , where is a compact separable metric…
On low for speed oracles
Laurent Bienvenu, Rod Downey
Relativizing computations of Turing machines to an oracle is a central concept in the theory of computation, both in complexity theory and in computability theory(!). Inspired by l…
Multiple Recurrence and Algorithmic Randomness
Rodney G. Downey, Satyadev Nandakumar, Andre Nies
This work contributes to the programme of studying effective versions of "almost everywhere" theorems in analysis and ergodic theory via algorithmic randomness. We determine the le…
Integer Valued Betting strategies and Turing Degrees
George Barmpalias, Rod G. Downey, Michael McInerney
Betting strategies are often expressed formally as martingales. A martingale is called integer-valued if each bet must be an integer value. Integer-valued strategies correspond to…