We extend a logical characterization of PSPACE due to Makowsky and Pnueli by showing that their logic has a particular
normal form which implies that the Generalized Hex problem is complete for PSPACE via very restricted logical reductions.
We also show that this normal form result fails in the absence of a built-in successor relation.
Arratia, A.; Stewart, I. Generalized Hex and logical characterizations of polynomial space. "Information processing letters", 1997, vol. 63, núm. 3, p. 147-152.