Random unary predicates: Almost sure theories and countable models

Joel H. Spencer, Katherine St John

Research output: Contribution to journalArticlepeer-review


Let Un, p be the random unary predicate and Tk be the almost sure first-order theory of Un, p under the linear ordering, where k is a positive integer and n-1/k ≪p(n) ≪ n-1/(k + 1). For each k, we give an axiomatization for the theory Tk. We find a model ℳk of Tk of order type roughly that of Zk and show that no other models of Tk exist of smaller size.

Original languageEnglish (US)
Pages (from-to)229-248
Number of pages20
JournalRandom Structures and Algorithms
Issue number3-4
StatePublished - 1998

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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