5 papers
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…
Weakly 2-randoms and 1-generics in Scott sets
Linda Brown Westrick
Let be a Scott set, or even an -model of . Then for each , either there is that is weakly 2-random relative to , or there is tha…
Dimension 1 sequences are close to randoms
Noam Greenberg, Joe Miller, Alexander Shen +1
We show that a sequence has effective Hausdorff dimension 1 if and only if it is coarsely similar to a Martin-Löf random sequence. More generally, a sequence has effective dimensio…
Finding bases of uncountable free abelian groups is usually difficult
Noam Greenberg, Dan Turetsky, Linda Brown Westrick
We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally…
Effectiveness of Hindman's theorem for bounded sums
Damir D. Dzhafarov, Carl G. Jockusch, Reed Solomon +1
We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified fin…