Finite h-dimension does not imply expressive completeness

Journal of Philosophical Logic 23 (5):535 - 573 (1994)
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
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DOI 10.1007/BF01049409
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Past, Present and Future.Arthur Prior - 1967 - Clarendon Press.
Time and Modality.A. N. Prior - 1955 - Greenwood Press.

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