Wang Wei: The definability strength of combinatorial principles

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 4 February 2015, 17:00 hrs

Room: S17#05-11, Department of Mathematics, NUS

Speaker: Wang Wei, Sun Yat-Sen University, Guangzhou

Title: The definability strength of combinatorial principles

In recent years people have extensively studied the provability
strength of combinatorial principles related to Ramsey’s theorem. In many
cases, the provability strength of a combinatorial principle is reflected
by its computability strength in the following sense: if solutions of
related combinatorial problems can serve as oracles to compute certain
complicated sets then the combinatorial principle is of strong provability
strength. In this talk, we introduce a different way to analyze strength
of combinatorial principles, by examing whether solutions of related
problems can help simplify certain definability problems. This approach
turns out to be useful in the reverse mathematics of combinatorics.


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