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\iteman{io-port 02098245}
\itemau{Nebesk\'y, Ladislav}
\itemti{The directed geodetic structure of a strong digraph.}
\itemso{Czech. Math. J. 54, No. 1, 1-8 (2004).}
\itemab
Summary: By a ternary structure we mean an ordered pair $(U_0, T_0)$, where $U_0$ is a finite nonempty set and $T_0$ is a ternary relation on~ $U_0$. A ternary structure $(U_0, T_0)$ is called here a directed geodetic structure if there exists a strong digraph~ $D$ with the properties that $V(D) = U_0$ and $ T_0 (u, v, w) \quad \text {if and only if} \quad d_D (u, v) + d_D (v, w) = d_D (u, w) $ for all $u, v, w \in U_0$, where $d_D$~ denotes the (directed) distance function in~ $D$. It is proved in this paper that there exists no sentence {\bf s} of the language of first-order logic such that a ternary structure is a directed geodetic structure if and only if it satisfies {\bf s}.
\itemrv{~}
\itemcc{}
\itemut{strong digraph; directed distance; ternary relation; finite structure}
\itemli{doi:10.1023/B:CMAJ.0000027243.70276.51}
\end