Abstract:
We define a new type of two player game occurring on a tree. The tree may
have no root and may have arbitrary degrees of nodes. These games extend the
class of games considered by Gurevich-Harrington in [5]. We prove that in the
game one of the players has a winning strategy which depends on finite bounded
information about the past part of a play and on future of each play that
is isomorphism types of tree nodes. This result extends further the Gurevich-
Harrington (GH) determinacy theorem from [5].