In standard logic, propositions are considered to be either true or false. However, a fundamental aspect of the human condition is that nobody can ever determine with absolute certainty whether a proposition about the world is true or false. In addition, whenever the truth of a proposition is assessed, it is always done by an individual, and it can never be considered to represent a general and...

The article starts with a brief survey of Unprovability Theory as of summer 2006. Then, as an illustration of the subject’s model-theoretic methods, we re-prove threshold versions of unprovability results for the Paris-Harrington Principle and the Kanamori-McAloon Principle using indiscernibles. In addition, we obtain a short accessible proof of unprovability of the ParisHarrington Principle. T...

Nearly fifty years after the introduction of skew Brownian motion by Itô and McKean (1963), the first passage time distribution remains unknown. In this paper, we first generalize results of Pitman and Yor (2001) and Csáki and Hu (2004) to derive formulae for the distribution of ranked excursion heights of skew Brownian motion, and then use this result to derive the first passage time distribut...