29 citations · 32 across the 6 of their papers we have counts for
9 papers
Open Problems in Computability Theory and Descriptive Set Theory
George Barmpalias, Nikolay Bazhenov, Chi Tat Chong +11
These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Computability Theory and Descriptive Set Theory, June 16-20, 2025. The problems are…
Randomness below complete theories of arithmetic
George Barmpalias, Wei Wang
We show that degrees containing a complete extensions of arithmetic have the random join property: they are the supremum of any random real they compute, with another random real.…
Conservation Strength of The Infinite Pigeonhole Principle for Trees
Chitat Chong, Wei Wang, Yue Yang
Let be the combinatorial principle stating that every finite coloring of the infinite full binary tree has a homogeneous isomorphic subtree. Let a…
Pathwise-random trees and models of second-order arithmetic
George Barmpalias, Wei Wang
A tree is pathwise-random if all of its paths are Martin-Lof random. We show that (a) no weakly 2-random real computes a perfect pathwise-random tree; it follows that the class of…
On Non-standard Models of Arithmetic with Uncountable Standard Systems
Wei Wang
In 1960s, Dana Scott gave a recursion theoretic characterization of standard systems of countable non-standard models of arithmetic, i.e., collections of sets of standard natural n…
Where Pigeonhole Principles meet König Lemmas
David Belanger, Chitat Chong, Wei Wang +2
We study the pigeonhole principle for -definable injections with domain twice as large as the codomain, and the weak König lemma for -definable trees in which every lev…
On The Computability of Perfect Subsets of Sets with Positive Measure
Chitat Chong, Wei Li, Wei Wang +1
A set 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 c…
Omitting cohesive sets
Wei Wang
We prove that if is a computable sequence of subsets of which admits no computable cohesive set, then no 3-generic computes any -cohesive set; and there exis…
Some logically weak Ramseyan theorems
Wei Wang
We study four families of consequences of Ramsey's Theorem from the viewpoint of reverse mathematics. The first, which we call the Achromatic Ramsey Theorem, is from a partition re…