### Abstract

Let U_{n, p} be the random unary predicate and T_{k} be the almost sure first-order theory of U_{n, 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 T_{k}. We find a model ℳ_{k} of T_{k} of order type roughly that of Z^{k} and show that no other models of T_{k} exist of smaller size.

Original language | English (US) |
---|---|

Pages (from-to) | 229-248 |

Number of pages | 20 |

Journal | Random Structures and Algorithms |

Volume | 13 |

Issue number | 3-4 |

State | Published - Oct 1998 |

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### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Mathematics(all)
- Applied Mathematics

### Cite this

*Random Structures and Algorithms*,

*13*(3-4), 229-248.

**Random unary predicates : Almost sure theories and countable models.** / Spencer, Joel H.; St John, Katherine.

Research output: Contribution to journal › Article

*Random Structures and Algorithms*, vol. 13, no. 3-4, pp. 229-248.

}

TY - JOUR

T1 - Random unary predicates

T2 - Almost sure theories and countable models

AU - Spencer, Joel H.

AU - St John, Katherine

PY - 1998/10

Y1 - 1998/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032221889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032221889&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 229

EP - 248

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 3-4

ER -