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On canonicity and completions of weakly representable relation algebras
Published online by Cambridge University Press: 12 March 2014
Abstract
We show that the variety of weakly representable relation algebras is neither canonical nor closed under Monk completions.
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- Copyright © Association for Symbolic Logic 2012
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REFERENCES
[1]Andréka, H., Weakly representable but not representable relation algebras, Algebra Universalis, vol. 32 (1994), pp. 31–43.CrossRefGoogle Scholar
[2]Andréka, H. and Bredikhin, D. A., The equational theory of union-free algebras of relations, Algebra Universalis, vol. 33 (1995), pp. 516–532.CrossRefGoogle Scholar
[3]Andréka, H., Goldblatt, R., and Németi, I., Relativised quantification: Some canonical varieties of sequence-set algebras, this Journal, vol. 63 (1998), pp. 163–184.Google Scholar
[4]Blackburn, P., de Rijke, M., and Venema, Y., Modal logic, Tracts in Theoretical Computer Science, Cambridge University Press, 2001.CrossRefGoogle Scholar
[5]Diestel, R., Graph theory, Graduate Texts in Mathematics, vol. 173, Springer-Verlag, Berlin, 1997.Google Scholar
[6]Gehrke, M., Harding, J., and Venema, Y., MacNeille completions and canonical extensions, Transactions of the American Mathematical Society, vol. 358 (2006), pp. 573–590.CrossRefGoogle Scholar
[7]Goldblatt, R., Metamathematics of modal logic, Reports on Mathematical Logic, vol. 6 (1976), pp. 41–77, reprinted in [9].Google Scholar
[8]Goldblatt, R., Varieties of complex algebras, Annals of Pure and Applied Logic, vol. 44 (1989), pp. 173–242.CrossRefGoogle Scholar
[9]Goldblatt, R., Mathematics of modality, Lecture notes, vol. 43, CSLI Publications, Stanford, CA, 1993.Google Scholar
[10]Goldblatt, R., Questions of canonicity, Trends in logic: 50years of Studia Logica (Hendricks, Vincent F. and Malinowski, Jacek, editors), Kluwer Academic Publishers, 2003, pp. 93–128.Google Scholar
[11]Goldblatt, R., Mathematical modal logic: A view of its evolution, Handbook of the history of logic (Gabbay, D. M. and Woods, J., editors), vol. 7, Elsevier, Amsterdam, 2006, pp. 1–98.Google Scholar
[12]Haiman, M., Arguesian lattices which are not linear, Bulletin of the American Mathematical Society, vol. 16 (1987), pp. 121–123.CrossRefGoogle Scholar
[13]Haiman, M., Arguesian lattices which are not type I, Algebra Universalis, vol. 28 (1991), pp. 128–137.CrossRefGoogle Scholar
[14]Henkin, L., Monk, J. D., and Tarski, A., Cylindric algebras part II, North-Holland, 1985.Google Scholar
[15]Hirsch, R. and Hodkinson, I., Relation algebras by games, Studies in Logic and the Foundations of Mathematics, vol. 147, North-Holland, Amsterdam, 2002.Google Scholar
[16]Hirsch, R., Hodkinson, I., and Maddux, R. D., Weak representations of relation algebras and relational bases, this Journal, vol. 76 (2011), pp. 870–882.Google Scholar
[17]Hodkinson, I., Atom structures of cylindric algebras and relation algebras, Annals of Pure and Applied Logic, vol. 89 (1997), pp. 117–148.CrossRefGoogle Scholar
[18]Hodkinson, I. and Mikulás, Sz., Non-finite axiomatizability of reducts of algebras of relations, Algebra Universalis, vol. 43 (2000), pp. 127–156.CrossRefGoogle Scholar
[19]Jónsson, B., Representation of modular lattices and of relation algebras, Transactions of the American Mathematical Society, vol. 92 (1959), pp. 449–464.CrossRefGoogle Scholar
[20]Jónsson, B. and Tarski, A., Boolean algebras with operators I, American Journal of Mathematics, vol. 73 (1951), pp. 891–939.CrossRefGoogle Scholar
[21]Maddux, R. D., A sequent calculus for relation algebras, Annals of Pure and Applied Logic, vol. 25 (1983), pp. 73–101.CrossRefGoogle Scholar
[22]Maddux, R. D., Relation algebras, Studies in Logic and the Foundations of Mathematics, vol. 150, North-Holland, Amsterdam, 2006.Google Scholar
[23]McKenzie, R., The representation of relation algebras, Ph.D. thesis, University of Colorado at Boulder, 1966.Google Scholar
[24]Monk, J. D., Completions of boolean algebras with operators, Mathematische Nachrichten, vol. 46 (1970), pp. 47–55.CrossRefGoogle Scholar
[25]Pécsi, B., Weakly representable relation algebras form a variety, Algebra Universalis, vol. 60 (2009), pp. 369–380.CrossRefGoogle Scholar
[26]Robert, A. M., A course in p-adic analysis, Graduate Texts, Springer, New York, 2000.CrossRefGoogle Scholar
[27]Wolter, F., Properties of tense logics, Mathematical Logic Quarterly, vol. 42 (1996), pp. 481–500.CrossRefGoogle Scholar