# 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. arXiv: math/9606230 DOI: 10.1002/(SICI)1098-2418(199612)9:4<351::AID-RSA1>3.3.CO;2-D MR: 1605415 -
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.

- Version 2011-11-14_12 (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}, mrnumber = {1605415}, mrclass = {05C80}, 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} }