Graduate student seminar – Very large finite numbers

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.

Goodstein sequences

Will Sladek, a student at Caltech, wrote an excellent introductory paper on incompleteness in PA, The termite and the tower. While Will was working on his paper, I wrote a short note, Goodstein’s function, on how to compute Goodstein’s function. Please let me know of any comments of corrections to either article.