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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 427–434 (Mi semr1066)  

Mathematical logic, algebra and number theory

Recognizability in pre-Heyting and well-composed logics

L. L. Maksimovaab, V. F. Yunab

a Sobolev Institute of Mathematics, 4, pr. Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia

Abstract: In this paper the problems of recognizability and strong recognizavility, perceptibility and strong perceptibility in extensions of the minimal Johansson logic $\mathrm{J}$ [1] are studied. These concepts were introduced in [2, 3, 4]. Although the intuitionistic logic Int is recognizable over $\mathrm{J}$ [2], the problem of its strong recognizability over $\mathrm{J}$ is not solved. Here we prove that Int is strong recognizable and strong perceptible over the minimal pre-Heyting logic Od and the minimal well-composed logic $\mathrm{JX}$. In addition, we prove the perceptibility of the formula $F$ over $\mathrm{JX}$. It is unknown whether the logic $\mathrm{J+F}$ is recognizable over $\mathrm{J}$.

Keywords: Recognizability, strong recognizability, minimal logic, pre-Heyting logic, Johansson algebra, Heyting algebra, superintuitionistic logic, calculus.

Funding Agency Grant Number
Siberian Branch of Russian Academy of Sciences I.1.1, проект № 0314-2019-0002


DOI: https://doi.org/10.33048/semi.2019.16.024

Full text: PDF file (151 kB)
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Bibliographic databases:

UDC: 510.6
MSC: 03B45
Received June 26, 2018, published March 29, 2019

Citation: L. L. Maksimova, V. F. Yun, “Recognizability in pre-Heyting and well-composed logics”, Sib. Èlektron. Mat. Izv., 16 (2019), 427–434

Citation in format AMSBIB
\Bibitem{MakYun19}
\by L.~L.~Maksimova, V.~F.~Yun
\paper Recognizability in pre-Heyting and well-composed logics
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 427--434
\mathnet{http://mi.mathnet.ru/semr1066}
\crossref{https://doi.org/10.33048/semi.2019.16.024}


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