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Galois theory for cylindric algebras and its applications

Author: Stephen D. Comer
Journal: Trans. Amer. Math. Soc. 286 (1984), 771-785
MSC: Primary 03G15; Secondary 06A15, 08B25, 20B35
MathSciNet review: 760986
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Abstract: A Galois correspondence between cylindric set algebras and permutation groups is presented in this paper. Moreover, the Galois connection is used to help establish two important algebraic properties for certain classes of finite-dimensional cylindric algebras, namely the amalgamation property and the property that epimorphisms are surjective.

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  • [1] Raymond Balbes, Projective and injective distributive lattices, Pacific J. Math. 21 (1967), 405–420. MR 0211927
  • [2] S. Comer, Some representation theorems and the amalgamation property in algebraic logic, Ph.D. Thesis, Univ. of Colorado, 1967.
  • [3] -, Galois theory and the amalgamation property in finite dimensional cylindric algebras, Notices Amer. Math. Soc. 15 (1968), 103.
  • [4] Stephen D. Comer, A sheaf-theoretic duality theory for cylindric algebras, Trans. Amer. Math. Soc. 169 (1972), 75–87. MR 0307908, 10.1090/S0002-9947-1972-0307908-3
  • [5] Paul R. Halmos, Injective and projective Boolean algebras, Proc. Sympos. Pure Math., Vol. II, American Mathematical Society, Providence, R.I., 1961, pp. 114–122. MR 0137671
  • [6] -, Boolean algebras, Van Nostrand, 1963; reprinted, Springer-Verlag, 1974.
  • [7] Leon Henkin, J. Donald Monk, and Alfred Tarski, Cylindric algebras. Part I, Studies in Logic and the Foundations of Mathematics, vol. 64, North-Holland Publishing Co., Amsterdam, 1985. With an introductory chapter: General theory of algebras; Reprint of the 1971 original. MR 781929
  • [8] Leon Henkin, J. Donald Monk, Alfred Tarski, Hajnal Andréka, and István Németi, Cylindric set algebras, Lecture Notes in Mathematics, vol. 883, Springer-Verlag, Berlin-New York, 1981. MR 639151
  • [9] Bjarni Jónsson, Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110–121 (1968). MR 0237402
  • [10] M. Krasner, Une generalisation de la notion de corps, J. Math. Pures Appl. 17 (1938), 367-385.
  • [11] -, Generalisation abstract de la theorie de Galois, Colloq. Internat. CNRS, No. 24, 1950, pp. 163-168.
  • [12] -, Les algèbres cylindriques, Bull Soc. Math. France 86 (1959), 315-319.
  • [13] Donald Monk, Model-theoretic methods and results in the theory of cylindric algebras, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 238–250. MR 0200159
  • [14] I. Németi, Surjectiveness of epis is equivalent to Beth definability in algebraic logic, Budapest, 1982. (preprint)
  • [15] R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056
  • [16] Don Pigozzi, Amalgamation, congruence-extension, and interpolation properties in algebras, Algebra Universalis 1 (1971/72), 269–349. MR 0300897

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Keywords: Cylindric algebras, Galois correspondence, amalgamation property, epimorphisms, injectives
Article copyright: © Copyright 1984 American Mathematical Society