Very weak zero one law for random graphs with order and random binary functions
Abstract
Let G_<(n,p) denote the usual random graph G(n,p) on a totally ordered set of n vertices. We will fix p=1/2 for definiteness. Let L^< denote the first order language with predicates equality (x=y), adjacency (x~y) and less than (x<y). For any sentence A in L^< let f_A(n) denote the probability that the random G_<(n,p) has property A. It is known Compton, Henson and Shelah [CHSh:245] that there are A for which f_A(n) does not converge. Here we show what is called a very weak zeroone law (from [Sh 463]): THEOREM: For every A in language L^<, lim_{n> infty}(f_A(n+1)f_A(n))=0.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1996
 DOI:
 10.48550/arXiv.math/9606230
 arXiv:
 arXiv:math/9606230
 Bibcode:
 1996math......6230S
 Keywords:

 Mathematics  Logic;
 Mathematics  Combinatorics
 EPrint:
 Random Structures Algorithms 9 (1996), 351358