Key points are not available for this paper at this time.
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent functions on proof trees as yet further proof trees satisfying a suitable analog of well-foundedness. Iterating this process allows us to represent higher order functions as well: since functions on proof trees are just proof trees themselves, these functions can easily be extended to act on proof trees which are themselves understood as functions. The corresponding system of ordinals parallels this, using higher order collapsing function.
Henry Towsner (Tue,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: