TY - JOUR

T1 - Categoricity Spectra for Polymodal Algebras

AU - Bazhenov, Nikolay

N1 - Funding Information: The author is grateful to Sergey Goncharov for fruitful discussions on the subject. The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal University. Also, the reported study was partially supported by RFBR, research Project No. 14-01-00376. Publisher Copyright: © 2016, Springer Science+Business Media Dordrecht.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - Autostability spectrum

KW - Boolean algebra with operators

KW - Categoricity spectrum

KW - Degree spectrum

KW - Polymodal algebra

KW - Turing computable embedding

UR - http://www.scopus.com/inward/record.url?scp=84961215297&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=29464459

U2 - 10.1007/s11225-016-9667-y

DO - 10.1007/s11225-016-9667-y

M3 - Article

AN - SCOPUS:84961215297

VL - 104

SP - 1083

EP - 1097

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 6

ER -