Can we express every transfinite concept constructively?

This is a discussion on Can we express every transfinite concept constructively? within the Theory forums in Theory and Concepts category; An interesting (I think) exposition and side-by-side: Bhupinder Singh Anand "Can we express every transfinite concept constructively?" http://arxiv.org/abs/math/0305249 << In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic in an appropriate, digital, computational language. In this paper we attempt - without addressing the question of whether or not Budnik succeeds in establishing his thesis convincingly - to identify dogmas of standard interpretations of classical mathematical theory that appear to be implicit in ...