Department of Computer Science
CUNY Graduate Center
33 West 42nd Street
New York
NY 10036 USA
parikh@csp.gc.cuny.edu
In these notes we shall be concerned with a semantic object which is a generalization of classical structures, Kripke structures and the regular *-structures of Ehrenfeucht-de Jongh. We shall start by showing how these different cases can be obtained by imposing different regularly conditions on the basic object (D-structures) and the semantics can then be directly interpreted into the semantics of D-structures. We shall then give a game-theoretic explanation of the semantics of the D-structures from which the finite model property of regular *-structures can be easily obtained. We go on to look at the proof theory of these objects.