In this post, we give a proof that does not interpret (without parameters) in the homogeneous poset
nor in the random graph
. The idea is to first show that every continuous action of
or
on a set is faithful or trivial. We show this by using the fact that
and
have least supports. Since
and
have an automorphism of order two and
does not, this proves that there is no nontrivial continuous action of
nor
on
.
Tag Archives: linearly ordered atoms
Orbit-finite systems of linear equations
Consider the following decision problem, over the equality symmetry.
Input: an orbit-finite system of linear equations over
Decide: does have a solution (not necessarily finitely-supported)?
Inspired by Eryk’s beautiful solution of this problem, we present another solution, using an amazing theorem from topological dynamics.