Random sparse unary predicates
Logic
2009-09-25 v1 Combinatorics
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)<< n^{-1} or for some positive integer k, n^{-1/k}<< p(n)<< n^{-1/(k+1)} or for all epsilon >0, n^{- epsilon}<< p(n) and n^{- epsilon}<< 1-p(n) or for some positive integer k, n^{-1/k}<< 1-p(n)<< n^{-1/(k+1)} or 1-p(n)<< 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.
Cite
@article{arxiv.math/9401214,
title = {Random sparse unary predicates},
author = {Saharon Shelah and Joel Spencer},
journal= {arXiv preprint arXiv:math/9401214},
year = {2009}
}