Definability in the h -quasiorder of labeled forests

Annals of Pure and Applied Logic 159 (3):318-332 (2009)
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Abstract

We prove that for any k≥3 each element of the h-quasiorder of finite k-labeled forests is definable in the ordinary first order language and, respectively, each element of the h-quasiorder of countable k-labeled forests is definable in the language Lω1ω, in both cases provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we characterize the automorphism groups of both structures and show that the structure of finite k-forests is atomic. Similar results hold true for two other relevant structures: the h-quasiorder of finite k-labeled trees and of finite k-labeled trees with a fixed label of the root element

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Hierarchies of Δ 0 2 ‐measurable k‐partitions.Victor L. Selivanov - 2007 - Mathematical Logic Quarterly 53 (4-5):446-461.

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