The Axiom of Choice and indeterminacy

It’s been a while since my last post — I apologize to any devoted fans who have been disappointed.

I’m taking a class on Descriptive Set Theory now.  Here is the proof of an interesting theorem from class: Assuming the Axiom of Choice, there exists an undetermined game.

Here, a game consists of two players, a pruned tree, and a payoff set A.  The players move alternately by picking an immediate extension of the last move.  Player I wins if, after infinitely many moves, they have created an element of A.  Player II wins otherwise.

For more information about these kinds of games, you may refer to this wikipedia entry: http://en.wikipedia.org/wiki/Determinacy.

Advertisements
This entry was posted in Descriptive Set Theory. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s