We develop a theory of (first-order) definability in the subword partial order in parallel with similar theories for the h-quasiorder of finite k-labeled forests and for the infix order. 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. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Kudinov, O. V., Selivanov, V. L., & Yartseva, L. V. (2010). Definability in the subword order. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6158 LNCS, pp. 246–255). https://doi.org/10.1007/978-3-642-13962-8_28
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