Regular Talk:
Undecidability in the Homomorphic Quasiorder  of Finite Labeled Forests

Abstract

We prove that the homomorphic quasiorder of finite k-labeled forests
has undecidable elementary theory for k> 2, in contrast to the known
decidability result for $k=2$. We establish also undecidablity (again
for every $k\geq 3$) of elementary theories of two other relevant
structures: the homomorphic quasiorder of finite k-labeled trees, and
of finite k-labeled trees with a fixed label of the root element.