# Constructive Ordinals and the Consistency of PA

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/