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Irreflexive Modality on a Chain of Type ω and P. S. Novikov Completeness

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Algebra and Logic Aims and scope

We consider a φ-logic L(ω) of a frame of order type ω endowed with an irreflexive operator. The irreflexive modality in LC was treated by the author in [Sib. Math. J., 55, No. 1, 185-190 (2014)] where it was shown that this modality on the class of finite chains, on the one hand, and on a single chain of order type ω, on the other hand, generates inconsistent φ-logics over LC. There, also, it was stated that L(ω) defines a new nonconstant connective in LC. Here we establish that the φ-logic L(ω) is Novikov complete over LC.

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Authors and Affiliations

  1. Udmurt State University, Izhevsk, Russia

    A. D. Yashin

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  1. A. D. Yashin
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Correspondence to A. D. Yashin.

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Translated from Algebra i Logika, Vol. 59, No. 6, pp. 702-718, November-December, 2020. Russian DOI: https://doi.org/10.33048/alglog.2020.59.605.

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Yashin, A.D. Irreflexive Modality on a Chain of Type ω and P. S. Novikov Completeness. Algebra Logic 59, 471–482 (2021). https://doi.org/10.1007/s10469-021-09618-y

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  • DOI: https://doi.org/10.1007/s10469-021-09618-y

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