On the Very Weak 0-1 Law for Random Graphs with Orders

Very Weak Zero One Law for Random Graphs with Order and Random Binary Functions Sh548

Let G<(n, p) denote the usual random graph G(n, p) on a totally ordered set of n vertices. (We naturally think of the vertex set as 1, . . . , n with the usual <). We will fix p = 12 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(n) = fA(n) denote the probability that the random G...

On 0, 1-laws and asymptotics of definable sets in geometric Fräıssé classes

We examine one consequence for the generic theory TC of a geometric Fräıssé class C when C has the 0, 1-law for first-order logic with convergence to TC itself. We show that in this scenario, if the asymptotic probability measure in play is not terribly exotic, then C is “very close” to being a 1-dimensional asymptotic class—so that TC is supersimple of finite SU -rank. Introduction. In much of...

Very weak zero one law for random graphs with order and random binary functions

The weak and strong laws of large numbers

converges in probability to 0. A strong law of large numbers is a statement that (1) converges almost surely to 0. Thus, if the hypotheses assumed on the sequence of random variables are the same, a strong law implies a weak law. We shall prove the weak law of large numbers for a sequence of independent identically distributed L random variables, and the strong law of large for the same hypothe...

Cubic symmetric graphs of orders $36p$ and $36p^{2}$

A graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. In this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.