# Characterizing sigma-scattered linear orders

Thu, 19/01/2017 - 10:00
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This is an expository presentation following the paper "Minimality of non $\sigma$-scattered orders" by Ishiu and Moore. In the first part of the talk we will introduce the invariant $\Omega(L)$ of a linear order $L$, and characterize $\sigma$-scattered linear orders in terms of this invariant. In the second part, we will prove under the forcing axiom $\mathsf{PFA}^+$ that any linear order which is minimal with respect to embedding among the non $\sigma$-scattered orders must be either a real or Aronszajn type.