Definability in the homomorphic quasiorder of finite labeled forests

Abstract

We prove that for any k ≥ 3 each element of the homomorphic quasiorder of finite k-labeled forests is definable, provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we show that the structure is atomic and characterize the automorphism group of the structure. Similar results hold true for 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. © Springer-Verlag Berlin Heidelberg 2007.