Hercules, Hydras and Peano Arithmetic
Friday 4th March, 2011 16:00-17:00 Mathematics Building, room 516
Gödel's Incompleteness Theorem tells us that there exist statements that are true but cannot be proven in any reasonably powerful mathematical system. An interesting question to ask is whether we can find examples of such statements. I will present two theorems that are expressible in the Peano axiomatisation of the natural numbers but not provable in it.