Boolean powers and stochastic spaces
Costas A. Drossos, George Markakis · Czech digital mathematics library · 1994
In [6], [7], D. Scott made the first attempt to connect Non standard Analysis and Boolean-valued models and at the same time he introduced Boolean Analysis, which had been developed subsequently mainly by G .Takeut i [10].Ill this paper we investigate the relationship between the Boolean power of R and the elementary stochastic space E in the sense of K a p p o s [3].We obtain here that these two spaces are isomorphic.In this way, we obtain a stochastic interpretation of the Boolean power structure.The development is similar to Takeuti's Boolean analysis.The main difference lies in the fact that we use a full Boolean-valued model, known as Boolean power, and a twostep procedure: First we develop a restrictive model (a discrete or a kind of first order model), the Boolean power, in which all the axioms of the reals can be transferred immediately, and then we complete it using Cauchy sequences or Dedekind cuts in order to get a model isomorphic to the stochastic space V.In this way, we avoid the general Scott-Solovay model and we get instead a model which is more appropriate for generalizing the Robinsonian Infinitesimal Analysis to Boolean Analysis.