Foreword from the Congress Chairs

We show that Tarski’s inductive definitions admit evidence-based interpretations of the first-order Peano Arithmetic PA that allow us to define the satisfaction and truth of the quantified formulas of PA constructively over the domain N of the natural numbers in two essentially different ways: (1) in terms of algorithmic verifiabilty; and (2) in terms of algorithmic computability. We argue that the algorithmically computable PA-formulas can provide a finitary interpretation of PA over the domain N of the natural numbers from which we may conclude that PA is consistent.