Games and Structures on aleph_2
As well as two person infinite games on, say, Baire space, one
may look at games building first order structures..
We look at such games, typically with more than order type omega
moves but which may not be determined.
If there are sufficient indiscernibles sets in the universe, then a player
be seen to have a winning strategy.
This can yield results on combinatorial properties at small cardinals, that
are more usually observed at larger ones.