# Sh:548

• Shelah, S. (1996). Very weak zero one law for random graphs with order and random binary functions. Random Structures Algorithms, 9(4), 351–358.
• 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=\frac{1}{2} for definiteness. Let L^< denote the first order language with predicates equality (x=y), adjacency (x\sim 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 zero-one law (from [Sh 463]):

THEOREM: For every A in language L^<, \lim_{n\rightarrow\infty}(f_A(n+1)-f_A(n))=0.

• Current version: 2011-11-14_10 (8p) published version (9p)
Bib entry
@article{Sh:548,
author = {Shelah, Saharon},
title = {{Very weak zero one law for random graphs with order and random binary functions}},
journal = {Random Structures Algorithms},
fjournal = {Random Structures \& Algorithms},
volume = {9},
number = {4},
year = {1996},
pages = {351--358},
issn = {1042-9832},
doi = {10.1002/(SICI)1098-2418(199612)9:4<351::AID-RSA1>3.3.CO;2-D},
mrclass = {05C80},
mrnumber = {1605415},
mrreviewer = {Tomasz J. {\L}uczak},
doi = {10.1002/(SICI)1098-2418(199612)9:4<351::AID-RSA1>3.3.CO;2-D},
note = {\href{https://arxiv.org/abs/math/9606230}{arXiv: math/9606230}},
arxiv_number = {math/9606230},
keyword = {0-1 laws}
}