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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, Issue 3, Pages 28–39 (Mi vuu437)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Axiomatics of P. S. Novikov complete extensions of the superintuitionistic logic $L2$ in the language containing an additional constant

A. K. Koshcheeva

Department of Algebra and Topology, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
Full-text PDF (260 kB) Citations (1)
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Abstract: The Novikov problem for a superintuitionistic logic $L$ is to describe the class of all maximal conservative (i.e. P. S. Novikov complete) extensions of $L$ in the language with additional logical connectives and logical constants. Since the family of all superintuitionistic logics has the power of the continuum, it is sensible to apply the P. S. Novikov problem to superintuitionistic logics which for one reason or other have already come to researchers' attention.
In particular, there are three so-called pretabular superintuitionistic logics (i.e. non-tabular, but all their own extensions are tabular). One of them – the logic $L2$ – is characterized by the class of finite rooted linearly ordered sets of depth 2. It is established that for superintuitionistic logic $L2$ in the language with one additional constant there are exactly five P. S. Novikov complete extensions; their semantic description is given.
In this paper we propose an explicit axiomatics for each of the five existing P. S. Novikov complete extensions of the superintuitionistic logic $L2$ in the language containing an additional constant.
Keywords: the superintuitionistic logic $L2$, a new logical constant, an explicit axiomatics of Novikov-complete extensions.
Received: 27.08.2014
Document Type: Article
UDC: 510.64
MSC: 03B55, 03B60
Language: Russian
Citation: A. K. Koshcheeva, “Axiomatics of P. S. Novikov complete extensions of the superintuitionistic logic $L2$ in the language containing an additional constant”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 3, 28–39
Citation in format AMSBIB
\Bibitem{Kos14}
\by A.~K.~Koshcheeva
\paper Axiomatics of P.\,S.~Novikov complete extensions of the superintuitionistic logic $L2$ in the language containing an additional constant
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2014
\issue 3
\pages 28--39
\mathnet{http://mi.mathnet.ru/vuu437}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:69
     
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