Random sparse unary predicates

Saharon Shelah; Joel Spencer

doi:10.1002/rsa.3240050302

Random sparse unary predicates

Saharon Shelah^*
, Joel Spencer

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Random unary predicates U on [n] holding with probability p are examined with respect to sentences A in a first‐order language containing U and “less than.” When p = p(n) satisfies n^k+1 ≪ 1 ≪ np^k it is shown that Pr[A] approaches a limit dependent only on k and A. In a similar circular model the limit is shown to be zero or one. © 1994 John Wiley & Sons, Inc.

Original language	English
Pages (from-to)	375-394
Number of pages	20
Journal	Random Structures and Algorithms
Volume	5
Issue number	3
DOIs	https://doi.org/10.1002/rsa.3240050302
State	Published - Jul 1994

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title = "Random sparse unary predicates",

abstract = "Random unary predicates U on [n] holding with probability p are examined with respect to sentences A in a first‐order language containing U and “less than.” When p = p(n) satisfies nk+1 ≪ 1 ≪ npk it is shown that Pr[A] approaches a limit dependent only on k and A. In a similar circular model the limit is shown to be zero or one. {\textcopyright} 1994 John Wiley \& Sons, Inc.",

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AB - Random unary predicates U on [n] holding with probability p are examined with respect to sentences A in a first‐order language containing U and “less than.” When p = p(n) satisfies nk+1 ≪ 1 ≪ npk it is shown that Pr[A] approaches a limit dependent only on k and A. In a similar circular model the limit is shown to be zero or one. © 1994 John Wiley & Sons, Inc.

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Random sparse unary predicates

Abstract

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