Today I gave a talk at the Graduate student seminar on some recent combinatorial results that produce sequences that grow very fast (in a precise sense). The talk is titled Very large finite numbers and here is the .pdf file.
It is based on two recent papers of mine that can be found on my papers page: Regressive functions on pairs, that has been submitted to the European Journal of Combinatorics, and Goodstein’s function, that appeared in Revista Colombiana de Matemáticas 41 (2)(2007), 381-391.
For a nice introduction to incompleteness and Goodstein’s theorem, see Will Sladek’s paper here.
A kind of library 