  In this paper the limit probabilities of first-order properties are studied.
The random graph $G(n,p)$ {\it obeys Zero-One $k$-Law} if for each first-order
property with quantifier depth not greater than $k$ its probability tends to 0
or tends to 1. We found an explicit interval to the left of any rational point
on which the Zero-One $k$-Law holds. We also proved, that if $t/s$ is a
rational number with numerator not greater than 2, then logarithm of our
interval's length has the same asymptotics up to a constant factor (when
$n\rightarrow\infty$) as logarithm of the biggest interval with right end at
$(t/s)$ on which Zero-One $k$-Law holds.
