Jh. Spencer et K. Stjohn, RANDOM UNARY PREDICATES - ALMOST SURE THEORIES AND COUNTABLE MODELS, Random structures & algorithms, 13(3-4), 1998, pp. 229-248
Let U-n,U-p be the random unary predicate and T-k be the almost sure f
irst-order theory of U-n,U-p under the linear ordering, where k is a p
ositive integer and n(-1/k) much less than p(n) much less than (-1/(k1)). 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 n
o other models of T-k exist of smaller size. (C) 1998 John Wiley & Son
s, Inc.