Studia Logica

, Volume 104, Issue 6, pp 1083–1097 | Cite as

Categoricity Spectra for Polymodal Algebras

  • Nikolay BazhenovEmail author


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.


Polymodal algebra Boolean algebra with operators Categoricity spectrum Autostability spectrum Degree spectrum Turing computable embedding 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Kazan Federal UniversityKazanRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia

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