Graduate Student Colloquium
Brandon Doherty, Department of Pure Mathematics, University of Waterloo
"Goodstein sequences and the Hydra game"
Gödel's incompleteness theorem proves the existence of certain statements about the natural numbers that can be neither proven nor disproven using basic first-order arithmetic. The kinds of statements constructed in the standard proof of the incompleteness theorem, however, are extremely technical, and not very interesting in and of themselves.