L. Westrick

activity

20162020

collaborators

Showing math.LOShow all

8 papers · 1 filter

math.LO2020

Luzin's (N) and randomness reflection

Arno Pauly, Linda Westrick, Liang Yu

We show that a computable function $f : R \to R$ has Luzin's property (N) if and only if it reflects $Π_{1}^{1}$ -randomnes, if and only if it reflects $Δ^1_1(\mathc…

math.LO2020

A note on the diamond operator

Linda Westrick

We show that if $1 \leq_{W} F$ and $F ⋆ F \leq_{W} F$ , then $F^{⋄} \leq_{W} F$ , where $⋆$ and $⋄$ are the following operations in the Weihrauch lattice: $⋆$ is th…

math.LO2019

Three topological reducibilities for discontinuous functions

Adam R. Day, Rod Downey, Linda Brown Westrick

We define a family of three related reducibilities, $\leq_{T}$ , $\leq_{tt}$ and $\leq_{m}$ , for arbitrary functions $f, g : X \to R$ , where $X$ is a compact separable metric…

math.LO2018

The determined property of Baire in reverse math

Eric P. Astor, Damir Dzhafarov, Antonio Montalbán +2

We define the notion of a determined Borel code in reverse math, and consider the principle $D P B$ , which states that every determined Borel set has the property of Baire. We show t…

math.LO2017

Weakly 2-randoms and 1-generics in Scott sets

Linda Brown Westrick

Let $S$ be a Scott set, or even an $ω$ -model of $WWKL$ . Then for each $A \in S$ , either there is $X \in S$ that is weakly 2-random relative to $A$ , or there is $X \in S$ tha…

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…