Measuring the Power of Arithmetical Theories

Abstract: This thesis discusses the possibility to measure the power of extentions of Peano Aritmetic, P A. It consists of three parts, an introduction and two separately written papers. In the introduction we present the problem and briefly give an account of van Lambalgen's and raatikainen's criticism of gnenralization of two versions of Chaitin's incompleteness theorem, and reinforces the above mentioned criticism. The second paper is the main paper of the thesis, and here, using the modal logic GL, we design a measure of the power, in terms of the capacity to prove theorems, of an important set of extentions of P A.