Random unary predicates: Almost sure theories and countable models

Let Un,p be the random unary predicate and Tk 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.

• Type: Journal
• Year: 1998
• Where: RSA
• Authors: Joel Spencer, Katherine St. John
• Keywords: Random Unary Predicate, RSA 1998, Sure first-order Theory, Theory Tk