Weak Ehrenfeucht-Fraïssé Games

In this paper we define a game which is played between two players
I and II on two mathematical structures A and B. The players choose elements
from both structures in moves, and at the end of the game the player II wins if
the chosen structures are isomorphic. Thus the difference of this to the ordinary
Ehrenfeucht-Fra¨ıss´e game is that the isomorphism can be arbitrary, whereas in
the ordinary EF-game it is determined by the moves of the players. We
investigate determinacy of the weak EF-game for different (the length of the
game) and its relation to the ordinary EF-game.