# Justin Moore: There may be no minimal non $\sigma$-scattered linear order

Place: Fields Institute (Stewart Library)

Date: March 28th, 2016 (14:00-15:00)

Speaker: Justin Moore

Title: There may be no minimal non $\sigma$-scattered linear order

Abstract:  In this talk we demonstrate that it is consistent that there is no linear order which is minimal with respect to being non $\sigma$-scattered.This shows a theorem of Laver, which asserts that the $\sigma$-scattered linear orders are well quasi-ordered is sharp. If time permits we will also prove that $PFA^+$ implies that every non $\sigma$-scattered linear order either contains a real type, an Aronszajn type, or a ladder system indexed by a stationary set, equipped with either the lexicographic of reverse lexicographic order. This is joint work with Hossein Lamei Ramandi.