I have done some work in this area, mainly to try to understand the
subject. In this block I include two published papers, one set of
notes (which ramble a bit), and two unpublished papers (which in their
present state are not ready for publication). I also include the
slides of a talk that I gave at the Leeds meeting in July 09.
A pre-publication version of the paper
A comparison of two systems of ordinal notations
Archive for Math. Logic 34 (2004) 65-83.
Comparison.pdf
.
A pre-publication version of the paper
Fruitful and helpful functions
Archive for Math. Logic 47 (2008) 677-709.
Fruitful.pdf
.
A long set of notes
Iteration templates as generalized ordinal notations
IterTemplate.pdf
.
First unpublished paper
An applied lambda-calculus for iteration templates
LambdaH.pdf
.
Second unpublished paper
Generating ordinal notations from below with a non-recursive
construction of the Schutte brackets
FromBelow.pdf
.
And the Leeds slides
OrdSlides.pdf
.