Random sparse unary predicates

Saharon Shelah; Joel Spencer

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arXiv · math/9401214

Random sparse unary predicates

Saharon Shelah·Joel Spencer

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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.

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BibTeX RIS

Saharon Shelah, Joel Spencer. 1994-01-15. Random sparse unary predicates. https://arxiv.org/abs/math/9401214

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