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Categoricity Spectra for Polymodal Algebras

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Abstract

We investigate effective categoricity for polymodal algebras (i.e., Boolean algebras with distinguished modalities). We prove that the class of polymodal algebras is complete with respect to degree spectra of nontrivial structures, effective dimensions, expansion by constants, and degree spectra of relations. In particular, this implies that every categoricity spectrum is the categoricity spectrum of a polymodal algebra.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Av., 630090, Novosibirsk, Russia

    Nikolay Bazhenov

  2. Kazan Federal University, 18 Kremlevskaya St., 420008, Kazan, Russia

    Nikolay Bazhenov

  3. Novosibirsk State University, 2 Pirogova St., 630090, Novosibirsk, Russia

    Nikolay Bazhenov

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  1. Nikolay Bazhenov
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Bazhenov, N. Categoricity Spectra for Polymodal Algebras. Stud Logica 104, 1083–1097 (2016). https://doi.org/10.1007/s11225-016-9667-y

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