Finite H-dimension does not imply expressive completeness

A conjecture of Gabbay (1981) states that any class of flows of time having the property known as finite H-dimension admits a finite set of expressively complete one-dimensional temporal connectives. Here we show that the class of ‘circular’ structures refutes the generalisation of this conjecture to Kripke frames. We then construct from this class, by a general method, a new class of irreflexive transitive flows of time that refutes the original conjecture. Our paper includes full descriptions of a method for establishing finite H-dimension for a class of structures and of the technique for extending finite H-dimension to other classes, and an introduction surveying the area of expressive completeness. Published in Journal of Philosophical Logic 23 (1994) 535–573. Publisher’s pdf available at http://www.springerlink.com/content/rj18m4r644q61576/ fulltext.pdf