Probabilities on first order models

Abstract

It is known that set algebras corresponding to first order models (i.e cylindric set algebras associated with first order interpretations) are not ?-closed, but closed w.r.t. certain infima and suprema i.e. [FORMULA] and [FORMULA] for any infinite subsequence y1, y2,... yi,... of the individuum variables in the language. We investigate probabilities denned on these set algebras and being continuous w.r.t. the suprema and infima in (*). We can not use the usual technics, because these suprema and infima are not the usual unions and intersections of sets. These probabilities are interesting in computer science among others, because the probabilities of the quantifier-free formulas determine that of any formula and the probabilities of the former ones can be measured by statistical methods. .