Sets and Probability

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets

Triangulating non-Archimedean probability

We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.publishe