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Amalgamation of polyadic algebras


Author: James S. Johnson
Journal: Trans. Amer. Math. Soc. 149 (1970), 627-652
MSC: Primary 02.48
DOI: https://doi.org/10.1090/S0002-9947-1970-0284319-9
MathSciNet review: 0284319
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Abstract: The main result of the paper is that for I an infinite set, the class of polyadic I-algebras (with equality) has the strong amalgamation property; i.e., if two polyadic I-algebras have a given common subalgebra they can be embedded in another algebra in such a way that the intersection of the images of the two algebras is the given common subalgebra.


References [Enhancements On Off] (What's this?)

  • [1] S. Comer, Some representation theorems and the amalgamation property in algebraic logic, Doctoral Dissertation, University of Colorado, Boulder, 1967.
  • [2] A. Daigneault, On automorphisms of polyadic algebras, Trans. Amer. Math. Soc. 112 (1964), 84-130. MR 29 #45. MR 0162741 (29:45)
  • [3] -, Freedom in polyadic algebras and two theorems of Beth and Craig, Michigan Math. J. 11 (1964), 129-135. MR 29 #3408. MR 0166130 (29:3408)
  • [4] -, Théorie des modèles en logique mathématique, Séminaire de mathématiques supérieures, Université de Montréal, 1963.
  • [5] A. Daigneault and D. Monk, Representation theory for polyadic algebras, Fund. Math. 52 (1963), 151-176. MR 27 #1358. MR 0151373 (27:1358)
  • [6] T. Frayne, A. Morel and D. Scott, Reduced direct products, Fund. Math. 51 (1962/63), 195-228. MR 26 #28. MR 0142459 (26:28)
  • [7] G. Grätzer, Universal algebra, University Series in Higher Mathematics, Van Nostrand, Princeton, N. J., 1968.
  • [8] P. Halmos, Algebraic logic. II: Homogeneous locally finite polyadic Boolean algebras of infinite degree, Fund. Math. 43 (1956), 255-325. MR 19, 112. MR 0086029 (19:112d)
  • [9] P. Halmos, Algebraic logic. IV: Equality in polyadic algebras, Trans. Amer. Math. Soc. 86 (1957), 1-27. MR 19, 830. MR 0090564 (19:830d)
  • [10] -, Algebraic logic, Chelsea, New York, 1962. MR 24 #A1808.
  • [11] L. Henkin, D. Monk and A. Tarski, Cylindric algebras. Vol. I, North-Holland, Amsterdam, (to appear).
  • [12] L. Henkin and A. Tarski, ``Cylindric algebras,'' in Lattice theory, Proc. Sympos. Pure Math., vol. 2, Amer. Math. Soc., Providence, R. I., 1961, pp. 83-113. MR 23 #A1564. MR 0124250 (23:A1564)
  • [13] J. S. Johnson, Amalgamation of polyadic algebras, Abstract #644-8, Notices Amer. Math. Soc. 14 (1967), 361.
  • [14] H. J. Keisler, A complete first-order logic with infinitary predicates, Fund. Math. 52 (1963), 177-203. MR 27 #2399. MR 0152419 (27:2399)
  • [15] H. Rasiowa and R. Sikorski, The mathematics of metamathematics, Monogr. Mat., Tom 41, PWN, Warsaw, 1963. MR 29 #1149. MR 0163850 (29:1149)
  • [16] R. Sikorski, Boolean algebras, 2nd. ed., Ergebnisse der Mathematik und ihrer Grenzgebeite, Band 25, Academic Press, New York and Springer-Verlag, Berlin and New York, 1964. MR 31 #2178. MR 0177920 (31:2178)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0284319-9
Keywords: Amalgamation property, Beth's Theorem, Craig's interpolation theorem, logical constant, witness to quantifier, rich polyadic algebra
Article copyright: © Copyright 1970 American Mathematical Society

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