Joseph S. Miller

activity

20052026

most citedRandomness and Differentiability

55 citations · 133 across the 13 of their papers we have counts for

collaborators

17 papers

math.LO2026

Listing the hyperarithmetical functions

Joseph S. Miller, Gian Marco Osso, Isabella Scott

Given a countable Turing ideal $I \subseteq ω^{ω}$ , we say that $x$ is a list (resp. weak list) of $I$ if $I = {x^{[n]} : n \in ω}$ (resp. if $\mathcal{…

math.LO2023

Redundancy of information: lowering dimension

Jun Le Goh, Joseph S. Miller, Mariya I. Soskova +1

Let At denote the set of infinite sequences of effective dimension t. We determine both how close and how far an infinite sequence of dimension s can be from one of dimension t, me…

math.LO2019

Highness properties close to PA-completeness

Noam Greenberg, Joseph S. Miller, Andre Nies

Suppose we are given a computably enumerable object arise from algorithmic randomness or computable analysis. We are interested in the strength of oracles which can compute an obje…

math.LO2017

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…

math.LO2017

Martin-Löf reducibility and cost functions

Noam Greenberg, Joseph S. Miller, Andre Nies +1

Martin-Löf (ML)-reducibility compares $K$ -trivial sets by examining the Martin-Löf random sequences that compute them. We show that every $K$ -trivial set is computable from a c.e.\…

math.LO2017★ 4 cited

Computing from projections of random points: a dense hierarchy of subideals of the $K$ -trivial degrees