How to win some simple iteration games Original Research Article

We introduce two new iteration games: the game View the MathML source, which is a strengthening of the weak iteration game, and the game View the MathML source, which is somewhat stronger than View the MathML source but weaker than the full iteration game of length ω1. For a countable M elementarily embeddable in some Vη, with two players I and II, we can show that II wins View the MathML source and that I does not win View the MathML source.