Yiping Miao

(She/Her) PhD student at UC Berkeley Logic Group

pingping AT berkeley DOT edu

Papers

Submitted

• Dimension of Generic Reals [arxiv]
Abstract
This paper investigates the Hausdorff measure of certain sets of generics in computability theory. Let $\Gamma$ be the Turing ideal in which we take the dense open sets. The set of $\Gamma$-Cohen generics has measure positive if and only if the gauge function is not dominated by every element in $\Gamma$, under some mild restrictions on the gauge function. The set of $\Gamma$-Mathias generics and the set of $\Gamma$-Sacks generics have measure positive if and only if the gauge function eventually dominates every element in $\Gamma$. This gives some comparison between the behavior of reals in the set and the measure of the set.
• A Comparison of Gauge Dimension and Effective Dimension [arxiv]
Abstract
We characterize the gauge profiles of $\mathcal{D}_s$, the set of reals with effective dimension $s$, and $\mathcal{D}_{\leq s}$, the set of reals with effective dimension $\leq s$. Let $W(s)$ be the set of reals that are $s$- well approximable. This gives us a separation between $\mathcal{D}_{\leq s}$ and $W(2/s)$ in terms of Hausdorff measure.

Not Intended for Publications

• Subfields of R with Arbitrary Hausdorff Dimension, from MA

Work in Progress

• Randomness for Two Coordinates

Expository

• Master's Thesis: Some Model Theoretic Results in Set Theory[pdf]

Talks

• ...[Slides]

Seminars