[FOM] Hydra games?

[Peter Smith]

Ok, there's the foundations-significant Kirby/Paris hydra battle, where we 
can show that Hercules always wins, by a transfinite induction up to 
epsilon_0

Now, there must be lots of other hydra games -- maybe some of them even a 
bit interesting! -- that terminate (or at least terminate on best play) 
with a win for Hercules, and can be shown to do so by inductions along 
smaller ordinals.

Does anyone happen to know if there's a discussion out there of examples of 
such shorter games?

[Disclosure: I'm writing a chapter in which I want to work up to the 
Kirby/Paris example through just a few warm-exercises on simpler hydra 
games. I don't want to be re-inventing the wheel, and it would be nice to 
have some examples which are better than my so-far feeble efforts!]

-- 
Dr Peter Smith: Faculty of Philosophy, University of Cambridge

ps218 at cam.ac.uk
www.logicmatters.net