Today’s the last of three lectures on Gentzen’s second proof of the consistency of PA in my proof theory course.

a) Still looking for good resources on ordinal notations, esp., \(<\epsilon_0\), especially around the question how one can “see” that they are well-ordered without mentioning that they are order-isomorphic to \(\epsilon_0\)  Takeuti has a discussion in his textbook, anything else?

b) Some fun links:

Andrej Bauer’s Hydra game applet: http://math.andrej.com/2008/02/02/the-hydra-game/

David Madore’s ordinal visualizer: http://www.madore.org/~david/math/drawordinals.html

c) Looking for a good intro to Goodstein’s theorem and incompleteness in PA: Will Sladek’s paper linked from Andrés Caicedo’s blog: https://andrescaicedo.wordpress.com/2007/07/27/goodstein-sequences/