Sh:432

• Shelah, S., & Spencer, J. H. (1994). Random sparse unary predicates. Random Structures Algorithms, 5(3), 375–394. arXiv: math/9401214 DOI: 10.1002/rsa.3240050302 MR: 1277609
• Abstract:
  The main result is the following

  Theorem: Let $p=p(n)$ be such that $p(n)\in[0,1]$ for all $n$ and either $p(n)\ll n^{-1}$ or for some positive integer $k$, $n^{-1/k}\ll p(n)\ll n^{-1/(k+1)}$ or for all $\epsilon>0$, $n^{-\epsilon}\ll p(n)$ and $n^{-\epsilon}\ll 1-p(n)$ or for some positive integer $k$, $n^{-1/k}\ll 1-p(n)\ll n^{-1/(k+1)}$ or $1-p(n)\ll n^{-1}$. Then $p(n)$ satisfies the Zero-One Law for circular unary predicates. Inversely, if $p(n)$ falls into none of the above categories then it does not satisfy the Zero-One Law for circular unary predicates.

• Version 1994-01-28_10 (20p) published version (20p)

@article{Sh:432,
 author = {Shelah, Saharon and Spencer, Joel H.},
 title = {{Random sparse unary predicates}},
 journal = {Random Structures Algorithms},
 fjournal = {Random Structures \& Algorithms},
 volume = {5},
 number = {3},
 year = {1994},
 pages = {375--394},
 issn = {1042-9832},
 mrnumber = {1277609},
 mrclass = {03C13 (60F20)},
 doi = {10.1002/rsa.3240050302},
 note = {\href{https://arxiv.org/abs/math/9401214}{arXiv: math/9401214}},
 arxiv_number = {math/9401214}
}