2018/03/05 by Gunatilleka, Danul K.
#03C10 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1803.01831
We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs G(n,n-α) given by Laskowski in [7] extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin-Shi hypergraphs. In the process we give a method of constructing extensions whose `relative rank' is negative but arbitrarily small in context. We give a necessary and sufficient condition for the theory of a Baldwin-Shi hypergraph to have atomic models. We further show that for certain well behaved classes of theories of Baldwin-Shi hypergraphs, the existentially closed models and the atomic models correspond.