Definability in the Infix Order on Words
We develop a theory of (first-order) definability in the infix partial order on words in parallel with a similar theory for the h-quasiorder of finite k-labeled forests. In particular, any element is definable (provided that words of length 1 or 2 are taken as parameters), the first-order theory of the structure is atomic and computably isomorphic to the first-order arithmetic. We also characterize the automorphism group of the structure and show that any arithmetical predicate invariant under the automorphisms of the structure is definable in the structure.
KeywordsInfix order definability automorphism least fixed point first-order theory biinterpretability
Unable to display preview. Download preview PDF.
- [He93]Hertling, P.: Topologische Komplexitätsgrade von Funktionen mit endlichem Bild. Informatik-Berichte 152, Fernuniversität Hagen (1993)Google Scholar
- [KS09]Kudinov, O.V., Selivanov, V.L.: A Gandy theorem for abstract structures and applications to first-order definability. To appear in the LNCS volume of Computability in Europe 2009 Proceedings (2009)Google Scholar
- [KSZ08]Kudinov, O.V., Selivanov, V.L., Zhukov, A.V.: Definability in the h-quasiorder of labeled forests. Annals of Pure and Applied Logic (2008) doi:10.1016/j.apal.2008.09.026Google Scholar
- [Th90]Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, pp. 133–191 (1990)Google Scholar