# 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 followingTheorem: 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.

- published version (20p)

Bib entry

@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}, doi = {10.1002/rsa.3240050302}, mrclass = {03C13 (60F20)}, mrnumber = {1277609}, mrreviewer = {Peter G. Hinman}, doi = {10.1002/rsa.3240050302}, note = {\href{https://arxiv.org/abs/math/9401214}{arXiv: math/9401214}}, arxiv_number = {math/9401214} }