On 2/11/2013 3:28 AM, William Elliot wrote: > On Mon, 11 Feb 2013, fom wrote: >> The post is way too long, but the attempted application of the topology >> is at the very end. > > Yes, way to long, detailed, rambling and pointless. >
I am sorry you feel that way.
I see you asking set-theoretic questions occasionally.
Are you aware that the axiom of determinacy is characterized in terms of two-person games?
That post considered the construction of the real numbers using Dedekind cuts.
Toward the end of that post, for the purposes of constructing that topology, I broke up the state tables and re-interpreted the situation in terms of questions and determinations. That is very close to a two-person game.
I do not know whether or not that analysis can be "made pretty". And, I do not know if it can be made more relevant to the game-theoretic descriptions.
I doubt, however, that you can find any analysis of the real numbers that even hints at an explanation for the determinacy axioms in the context of any one of their classical definitions.
But, again, thank you for your help. It is greatly appreciated.