It is frequently claimed (see e.g. [Rav]) that the formalization of a mathematical proof requires a quality of understanding that subsumes all necessary acts for checking the proof and that,â€¦ (More)

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of trueâ€¦ (More)

Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standardâ€¦ (More)

A typical phenomenon for machine models of trans-finite computations is the existence of so-called lost melodies, i.e. real numbers x such that the characteristic function of the set {x} isâ€¦ (More)