By a ternary structure we mean an ordered pair (
U
0,
T
0), where
U
0is a
finitenonempty set and
T
0is 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
Dwith the properties that
V(
D) =
U
0and
T
0
(u,v, w)if and only if d
D
(u,v)+ d
D
(v,w)= d
D
(u, w)
for all
u,
v,
w
U
0, where
d
Ddenotes the (directed) distance function in
D. It is proved in this paper that there exists no sentence
sof the language of the first-order logic such that a ternary structure is a directed geodetic structure if and only if it satisfies
s.
strong digraph - directed distance - ternary relation - finite structure