Definability in the Subword Order

摘要

We develop a theory of (first-order) definability in the sub-word partial order in parallel with similar theories for the ft-quasiorder of finite fc-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.