Submission date: 18 June 2016

Abstract:

In the context of Hrushovski constructions we take a language L with a ternary relation R and consider the theory of the generic models M^*_α, of the class of finite L-structures equipped with predimension functions δ_α, for α in (0,1] ∩ Q. The theory of generic structures of non-AC smooth classes have been investigated from different points of view, including decidability and their power in interpreting known structures and theories. For a rational α in (0,1], first we prove that the theory of M^*_α admits a quantifier elimination down to a meaningful class of formulas, called `closure formulas' and on the other hand we prove that Th(M^*_α) does not have the finite model property.

Mathematics Subject Classification: 03C30 (Primary), 03C10 (Secondary)

Keywords and phrases:

Full text arXiv 1606.05750: pdf, ps.