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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - A. D. Yashin
TI  - Irreflexive modality on a chain of type $\omega$ and Novikov completeness
JO  - Algebra i logika
PY  - 2020
SP  - 702
EP  - 718
VL  - 59
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2020_59_6_a4/
LA  - ru
ID  - AL_2020_59_6_a4
ER  - 
%0 Journal Article
%A A. D. Yashin
%T Irreflexive modality on a chain of type $\omega$ and Novikov completeness
%J Algebra i logika
%D 2020
%P 702-718
%V 59
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2020_59_6_a4/
%G ru
%F AL_2020_59_6_a4
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/

[1] P. S. Novikov, Konstruktivnaya matematicheskaya logika s tochki zreniya klassicheskoi, Matem. logika i osnovaniya matem., Nauka, M., 1977

[2] D. P. Skvortsov, “Ob intuitsionistskom ischislenii vyskazyvanii s dopolnitelnoi logicheskoi svyazkoi”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 154–173

[3] Ya. S. Smetanich, “O polnote ischisleniya vyskazyvanii s dopolnitelnoi operatsiei ot odnoi peremennoi”, Tr. MMO, 9, 1960, 357–371

[4] Ya. S. Smetanich, “Ob ischisleniyakh vyskazyvanii s dopolnitelnoi operatsiei”, Dokl. AN SSSR, 139:2 (1961), 309–312 | Zbl

[5] M. Dummett, “A propositional calculus with denumerable matrix”, J. Symb. Log., 24:1 (1959), 97–106 | DOI | MR | Zbl

[6] L. L. Maksimova, “Predtablichnye superintuitsionistskie logiki”, Algebra i logika, 11:5 (1972), 558–570 | MR | Zbl

[7] A. D. Yashin, “Irrefleksivnaya modalnost kak novaya logicheskaya svyazka v logike Dammeta”, Sib. matem. zh., 55:1 (2014), 228–234 | MR | Zbl

[8] A. Yashin, “Dummett logic, irreflexive modality and Novikov completeness”, Larisa Maksimova on implication, interpolation, and definability, Outst. Contrib. Log., 15, ed. S. Odintsov, Springer, Cham, 2018, 319–337 | DOI | MR | Zbl

[9] R. I. Goldblatt, “Metamathematics of modal logic. I”, Rep. Math. Logic, 6 (1976), 41–77 | MR | Zbl

[10] R. I. Goldblatt, “Metamathematics of modal logic. II”, Rep. Math. Logic, 7 (1976), 21–52 | MR

[11] D. M. Gabbay, “On some new intuitionistic propositional connectives. I”, Stud. Log., 36:1/2 (1977), 127–139 | DOI | MR | Zbl