Abstract
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 the 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 every predicate invariant under the automorphisms of the structure is definable in the structure.
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Original Russian Text Copyright © 2010 Kudinov O. V., Selivanov V. L., and Yartseva L. V.
The first and second authors were supported by the DFG-RFBR (Grants 436 RUS 113/1002/01 and 09-01-91334), the first author was supported by the Russian Foundation for Basic Research (Grants 08-01-00336a and 09-01-12140_OFI_M), and all authors were supported by the Russian Foundation for Basic Research (Grant 07-01-00543a).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 575–583, May–June, 2010.
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Kudinov, O.V., Selivanov, V.L. & Yartseva, L.V. Definability in the structure of words with the inclusion relation. Sib Math J 51, 456–462 (2010). https://doi.org/10.1007/s11202-010-0047-y
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DOI: https://doi.org/10.1007/s11202-010-0047-y