Two proofs of the Halpern-Lauchli theorem

Speaker Biography

Yang Yue is a professor in the Department of Mathematics at the National University of Singapore. His research area is mathematical logic, especially computability theory and reverse mathematics. He and his collaborators have published many papers in top international academic journals such as the Journal of American Mathematical Society, Advances in Mathematics, Transactions of the American Mathematical Society, and the Journal of Symbolic Logic. He is also on the editorial board of the Journal of Mathematical Logic.

Abstract

I will give two proofs of the Halpern-Lauchli Theorem (HL). One is an elementary proof, which can be completed within the framework of and induction. This elementary proof is part of an ongoing project with collaborators Zhuang Zhida and Li Wei, which aims to explore the proof-theoretic strength of HL. The other proof is a forcing proof, based on Dobrinen's expression. This proof is very complex, in stark contrast to the elementary proof.