
Késako?
Here's a game, entitled « nonstandard gap », which lets you figure out if the person you're speaking to has a nonstandard mind, or  and surely it's the same thing  if they're secretely a set theorist.
This is a twoplayer game where Alice and Bob play in turns. At the th round, Alice sets forth an ordinal , then Bob proposes an ordinal , with the following constraints:
(1) 
Alice loses the game in the th round if Bob submits her a winning strategy, with proof that in less than a determined number of rounds after this th one, Alice won't be able to extend her sequence while observing the constraints (that is, we'll have for a certain ). Bob loses the game if he gives up or dies of thirst.
Example. Alice plays the number ;
Bob plays ;
Alice plays ;
Bob plays ;
Alice plays ;
Bob plays ;
Alice plays .
Bob then proposes the following winning strategy:
If Alice has just played the number
where , then Bob will play
where is the predecessor of in for the appropriate lexicographical ordering. Bob claims, with proof, that Alice will lose in at most additional rounds.
Question
Question
Remark. I never lost a game of nonstandard gap.