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 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.
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References
Barwise, J.: Admissible Sets and Structures. Springer, Berlin (1975)
Ershov, Y.L.: Definability and Computability. Plenum, New-York (1996)
Glaßer, C., Schmitz, H.: The Boolean Structure of Dot-Depth One. Journal of Automata, Languages and Combinatorics 6, 437–452 (2001)
Higman, G.: Ordering by divisibility in abstract algebras. Proceegings of London Mathematical Society 3, 326–336 (1952)
Hodges, W.: Model Theory. Cambridge Univ. Press, Cambidge (1993)
Kruskal, J.B.: The theory of well-quasi-ordering: a frequently discovered concept. J. Combinatorics Th. (A) 13, 297–305 (1972)
Kudinov, O.V., Selivanov, V.L.: A Gandy theorem for abstract structures and applications to first-order definability. In: Ambos-Spies, K., Löwe, B., Merke, W. (eds.) CiE 2009. LNCS, vol. 5635, pp. 290–299. Springer, Heidelberg (2009)
Kudinov, O.V., Selivanov, V.L.: Definability in the infix order on words. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 454–465. Springer, Heidelberg (2009)
Kuske, D.: Theories of orders on the set of words. RAIRO Theoretical Informatics and Applications 40, 53–74 (2006)
Lothaire, M.: Combinatorics on words, Cambridge Mathematical Library. Cambridge University Press, Cambridge (1997)
Moschovakis, Y.: Elementatry induction on abstract structures. North-Holland, Amsterdam (1974)
Nies, A.: Definability in the c.e. degrees: questions and results. Contemporary Mathematics 257, 207–213 (2000)
Selivanov, V.L.: A logical approach to decidability of hierarchies of regular star-free languages. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 539–550. Springer, Heidelberg (2001)
Vaught, R.A.: Axiomatizability by a schema. Journal of Symbolic Logic 32(4), 473–479 (1967)
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Kudinov, O.V., Selivanov, V.L., Yartseva, L.V. (2010). Definability in the Subword Order. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_28
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DOI: https://doi.org/10.1007/978-3-642-13962-8_28
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