Geodesic
Irreflexive modality on a chain of type $\omega$ and Novikov completeness
Algebra i logika, Tome 59 (2020) no. 6, pp. 702-718

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We consider a $\varphi$-logic $\mathcal{L}(\omega)$ of a frame of order type $\omega$ endowed with an irreflexive operator. The irreflexive modality in $LC$ was treated by the author in [Sib. Mat. Zh., 55, No. 1 (2014), 228–234] 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 $\omega$, on the other hand, generates inconsistent $\varphi$-logics over $LC$. There, also, it was stated that $\mathcal{L}(\omega)$ defines a new nonconstant connective in $LC$. Here we establish that the $\varphi$-logic $\mathcal{L}(\omega)$ is Novikov complete over $LC$.
Keywords: $\varphi$-logic, irreflexive modality, chain of order type $\omega$, Novikov completeness. 
@article{AL_2020_59_6_a4,
     author = {A. D. Yashin},
     title = {Irreflexive modality on a chain of type $\omega$ and {Novikov} completeness},
     journal = {Algebra i logika},
     pages = {702--718},
     publisher = {mathdoc},
     volume = {59},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_6_a4/}
}
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A. D. Yashin. Irreflexive modality on a chain of type $\omega$ and Novikov completeness. Algebra i logika, Tome 59 (2020) no. 6, pp. 702-718. http://geodesic.mathdoc.fr/item/AL_2020_59_6_a4/