Geodesic
Modeling arithmetic in the first-order language enriched with temporal quantifiers
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2016), pp. 5-19

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We investigate the classical first-order language with equality enriched by the modalities of the computational tree logic $\bf CTL^\ast$. As a semantics for it we consider serial Kripke frames with constant domains. We construct an embedding of the truth arithmetics into the set of all formulas that are valid in the class of such frames. Then, we obtain some corollaries concerned algorithmical, syntactical, and semantical properties for a large class of logic in the language.
Keywords: first-order logic, computational tree logic, recursive enumerability, Kripke semantics. 
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     author = {E. A. Kotikova and M. N. Rybakov},
     title = {Modeling arithmetic in the first-order language enriched with temporal quantifiers},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--19},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2016_4_a0/}
}
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E. A. Kotikova; M. N. Rybakov. Modeling arithmetic in the first-order language enriched with temporal quantifiers. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2016), pp. 5-19. http://geodesic.mathdoc.fr/item/VTPMK_2016_4_a0/