Abstract

In this paper we study some model theory for Gaifman probability structures. A classical result of Horn-Tarski concerning the extension of probabilities on Boolean algebras will allow us to prove some preservation theorems for probability structures, the model-companion of logical probability, etc. extending some classical results in eastern model theory.\\[0.2cm] Mathematics Subject Classification: 03C20, 03C90, 28A60.\\[0.2cm] Keywords: Gaifman probability structure, existentially closed probability structure, inductive probability, model-companion of a probability.