[FOM] Hydra games?

Jeffrey Sarnat jeffrey.sarnat at gmail.com
Sun May 23 16:58:21 EDT 2010

"Hydrae and Subsystems of Arithmetic" by Walter A. Carnielli and Michael 
Rathjen has a proof for omega_n (i.e. the exponential tower of n omegas). 
I don't know if it's available online, so you may have to get one of them 
to send it to you.


On Sun, 23 May 2010, Peter Smith wrote:

> 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
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