Definability in the Subword Order

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...

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Bibliographic Details
Published inPrograms, Proofs, Processes pp. 246 - 255
Main Authors Kudinov, Oleg V., Selivanov, Victor L., Yartseva, Lyudmila V.
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
automorphism
biinterpretability
definability
first-order theory
infix order
least fixed point
Subword order
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Summary: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.
ISBN:9783642139611
3642139612
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-13962-8_28