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- W4301431636 abstract "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 $nrightarrowinfty$) as logarithm of the biggest interval with right end at $(t/s)$ on which Zero-One $k$-Law holds." @default.
- W4301431636 created "2022-10-05" @default.
- W4301431636 creator A5023602402 @default.
- W4301431636 date "2016-02-01" @default.
- W4301431636 modified "2023-09-27" @default.
- W4301431636 title "Universal Zero-One $k$--Law" @default.
- W4301431636 doi "https://doi.org/10.48550/arxiv.1602.00510" @default.
- W4301431636 hasPublicationYear "2016" @default.
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