Geodesic
On tautologies in $\omega^+$-valued logic
Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 947-955 
L. L. Maksimova. On tautologies in $\omega^+$-valued logic. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 947-955. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a12/
@article{MZM_1975_17_6_a12,
     author = {L. L. Maksimova},
     title = {On tautologies in $\omega^+$-valued logic},
     journal = {Matemati\v{c}eskie zametki},
     pages = {947--955},
     year = {1975},
     volume = {17},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The connection is established in this paper between the tautologies of the $\omega^+$-valued predicate logic studied in [1] and the tautologies of m-valued logic for various $m<\omega$. As a consequence it is proven that the set of tautologies of $\omega^+$-valued predicate logic is an forallexist-set. An algorithm is constructed which, for any arbitrary formula of $\omega^+$-valued logic, recognizes whether or not that formula is an $\omega^+$-valued tautology; one axiomatization is proposed for the $\omega^+$-valued propositional logic.