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Abstract: 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 temporal connectives, but does not have the k-variable property for any finite k. 1 Introduction This paper is concerned with the relationship between the k-variable property and finite H- or Henkin-dimension. These are notions of `bounded ... (Update)
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BibTeX entry: (Update)
@misc{ hodkinson-kvariable,
author = "Ian Hodkinson and András Simon",
title = "The k-variable property is stronger than H-dimension k",
url = "citeseer.ist.psu.edu/283635.html" }
Citations (may not include all citations):140 Tense Logic and the Theory of Linear Order (context) - Kamp - 1968
97 A Formalization of Set Theory without Variables (context) - Tarski, Givant - 1987
85 Upper and lower bounds for first-order expressibility (context) - Immerman - 1982
52 Oxford University Press (context) - Gabbay, Hodkinson et al. - 1994
40 Definability with bounded number of bound variables - Immerman, Kozen - 1987
33 Many-dimensional Modal Logic (context) - Venema - 1992
33 Information and Computation (context) - Ph, Vardi et al. - 1992
17 Free Algebras and Decidability in Algebraic Logic (context) - N'emeti - 1986
7 Logical systems containing only a finite number of symbols (context) - Henkin - 1967
4 Finite variable logics - Hodkinson - 1993
3 London Mathematical Society Lecture Notes (context) - Cameron, Groups - 1990
2 dimension does not imply expressive completeness (context) - Hodkinson, H- - 1994
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