Convergence Laws for Very Sparse Random Structures with Generalized Quantifiers
Risto Kaila · Mathematical logic quarterly · 2002
We prove convergence laws for logics of the form , where is a properly chosen collection of generalized quantifiers, on very sparse finite random structures. We also study probabilistic collapsing of the logics , where is a collection of generalized quantifiers and k ∈ ℕ+, under arbitrary probability measures of finite structures.