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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…
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…