通用零一$k$ --定律
Universal Zero-One $k$--Law
摘要：
本文研究了一阶性质的极限概率。随机图$G(n,p)$ { \it服从Zero-One $k$ -Law}，如果对于每个量词深度不大于$k$的一阶属性，其概率趋于0或趋于1。我们发现了一个明确的区间的任何有理点的左边，在其上的0 - 1 $k$ -法律持有。我们还证明了，如果$t/s$是一个有理数，分子不大于2，那么我们的区间长度的对数有相同的渐近常数因子（当$n\rightarrow\infty$）的最大区间的对数，右端在$(t/s)$上的$k$零一定律成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
