Randomised structures and theories

18 January 2008
Itai Ben Yaacov
H. Jerome Keisler suggested to associate to each classical structure M a family of "random" structures consisting of random variables with values in M . Viewing the random structures as structures in continuous logic one is able to prove preservation results of various "good" model theoretic properties e.g., stability and dependence, from the original structure to its randomisation. On the other hand, simplicity is not preserved by this construction. The work discussed is mostly due to H. Jerome Keisler and myself (given enough time I might discuss some applications obtains in joint work with Alex Usvyatsov).