Decidability and undecidability of theories with a predicate for the primes.

P.T. Bateman, C.G Jockusch, Alan Woods

    Research output: Contribution to journalArticlepeer-review

    Abstract

    It is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure , where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of is decidable, where S is the successor function. The latter result is proved using a general result of A. L. Semenov on decidability of monadic theories, and a proof of Semenov's result is presented.
    Original languageEnglish
    Pages (from-to)672-687
    JournalJournal of Symbolic Logic
    Volume58
    DOIs
    Publication statusPublished - 1993

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