We establish a Gandy theorem for a class of abstract structures and deduce some corollaries, in particular the maximal definability result for arithmetical structures in the class. We also show that the arithmetical structures under consideration are biinterpretable (without parameters) with the standard model of arithmetic. As an example we show that for any k ≥ 3 a predicate on the quotient structure of the h-quasiorder of finite k-labeled forests is definable iff it is arithmetical and invariant under automorphisms. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Kudinov, O. V., & Selivanov, V. L. (2009). A Gandy theorem for abstract structures and applications to first-order definability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5635 LNCS, pp. 290–299). https://doi.org/10.1007/978-3-642-03073-4_30
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