Tag Archives: linearly ordered atoms

Least supports and non-interpretability

October 20, 2016 szymtor Leave a comment

In this post, we give a proof that $(\str Q,\le)$ does not interpret (without parameters) in the homogeneous poset $P$ nor in the random graph $R$ . The idea is to first show that every continuous action of $\aut P$ or $\aut R$ on a set is faithful or trivial. We show this by using the fact that $P$ and $R$ have least supports. Since $\aut P$ and $\aut R$ have an automorphism of order two and $\aut {\str Q,\le}$ does not, this proves that there is no nontrivial continuous action of $\aut P$ nor $\aut R$ on $\str Q$ .