arXiv subjects

Chitat Chong

Publications and source records attributed to Chitat Chong.

3 recordsLinked to original sources

arXiv2021

Conservation Strength of The Infinite Pigeonhole Principle for Trees

Let $\mathsf{TT}^1$ be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let $\mathsf{RT}^2_2$ and $\mathsf{WKL}_0$ denote respectively the principles of Ramsey's theorem for pairs and weak König's lemma. It is proved that $\mathsf{TT}^1+\mathsf{RT}^2_2+\mathsf{WKL}_0$ is $Π^0_3$-conservative over the base system $\mathsf{RCA}_0$. Thus over $\mathsf{RCA}_0$, $\mathsf{TT}^1$ and Ramsey's theorem for pairs prove the same $Π^0_3$-sentences.

math.LO↗

arXiv2019

Where Pigeonhole Principles meet König Lemmas

We study the pigeonhole principle for $Σ_2$-definable injections with domain twice as large as the codomain, and the weak König lemma for $Δ^0_2$-definable trees in which every level has at least half of the possible nodes. We show that the latter implies the existence of $2$-random reals, and is conservative over the former. We also show that the former is strictly weaker than the usual pigeonhole principle for $Σ_2$-definable injections.

math.LO↗

arXiv2018

On The Computability of Perfect Subsets of Sets with Positive Measure

A set $X \subseteq 2^ω$ with positive measure contains a perfect subset. We study such perfect subsets from the viewpoint of computability and prove that these sets can have weak computational strength. Then we connect the existence of perfect subsets of sets with positive measure with reverse mathematics.

math.LO↗