The k-variable property is stronger than H-dimension k

    I. Hodkinson and A Simon

    J. Philosophical Logic 26 (1997) 81--101.

    We study the notion of H-dimension and the formally stronger k-variable property, as considered by Gabbay and Immerman & Kozen. We exhibit a class of flows of time that has H-dimension 3, and admits a finite expressively complete set of one-dimensional connectives, but does not have the k-variable property for any finite k.