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Rectangular games

Published online by Cambridge University Press:  12 March 2014

Yde Venema*
Affiliation:
Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The, Netherlands. E-mail:[email protected]

Abstract

We prove that every rectangularly dense diagonal-free cylindric algebra is representable. As a corollary, we give finite, sound and complete axiomatizations for the finite-variable fragments of first order logic without equality and for multi-dimensional modal S5-logic.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Andréka, H., Givant, S., Mikulas, S., Nemeti, I., and Simon, A., Notions of density that imply representability in algebraic logic, Annals of Pure and Applied Logic, vol. 91 (1998), pp, 93190.Google Scholar
[2] Henkin, H., Monk, J. D., and Tarski, A., Cylindric algebras I & II, North-Holland, Amsterdam, 1971, 1985.Google Scholar
[3] Hirsch, R. and Hodkinson, I., Step by step—Building representations in algebraic logic, this Journal, vol. 62 (1997), pp. 225275.Google Scholar
[4] Jipsen, P., Discriminator varieties of boolean algebras with residuated operators. Algebraic methods in logic and computer science (Rauszer, C., editor), 1993, pp. 239252.Google Scholar
[5] Mikulás, S., Gabbay-style calculi, Proof theory of modal logic (Wansing, H., editor), 1996.Google Scholar
[6] Venema, Y., Derivation rules as anti-axioms in modal logic, this Journal, vol. 58 (1993), pp. 10031034.Google Scholar
[7] Venema, Y., Cylindric modal logic, this Journal, vol. 60 (1995), pp. 591623.Google Scholar
[8] Venema, Y., Rectangular games, Technical report, Mathematics Department, Victoria University Wellington, 1996, Research Report 96-176, 02 1996.Google Scholar