FO(TC) lower bounding games? Is anyone aware of any games/algebraic structures that provide lower-bounding methodologies for $FO(TC)$ formulae? I am aware of EF games as they apply to first-order and second-order statements, but would like to be able to determine lower bounds for $FO(TC)$ queries on finite models. Any help in this direction would be appreciated!
As mentioned above: question answered by reference to FO(TC) games presented in Finite Model Theory by Ebbinghaus and Flum.