On a sequence of random distance graphs subject to the zero-one law

It is known that an Erdős–Rényi random graph obeys a zero-one law for first-order properties. The study of these laws started in 1969 with the work of Yu. V. Glebskii, D. I. Kogan, M. I. Liogon'kii, and V. A. Talanov. We proved in our previous works that a random distance graph does not obey the zero-one law. In this paper a sequence of random distance graphs obeying the zero-one law is obtained.