Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Cylindric algebras and algebras of substitutions
HTML articles powered by AMS MathViewer

by Charles Pinter PDF
Trans. Amer. Math. Soc. 175 (1973), 167-179 Request permission

Abstract:

Several new formulations of the notion of cylindric algebra are presented. The class $C{A_\alpha }$ of all cylindric algebras of degree $\alpha$ is shown to be definitionally equivalent to a class of algebras in which only substitutions (together with the Boolean $+ , \cdot$, and $-$) are taken to be primitive operations. Then $C{A_\alpha }$ is shown to be definitionally equivalent to an equational class of algebras in which only substitutions and their conjugates (together with $+ , \cdot$, and $-$) are taken to be primitive operations.
References
    G. Birkhoff, On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (1935), 433-454.
  • William Craig, Unification and abstraction in algebraic logic, Studies in algebraic logic, Studies in Math., Vol. 9, Math. Assoc. Amer., Washington, D.C., 1974, pp. 6–57. MR 0376345
  • Paul R. Halmos, The basic concepts of algebraic logic, Amer. Math. Monthly 63 (1956), 363–387. MR 86028, DOI 10.2307/2309396
  • Paul R. Halmos, Algebraic logic. I. Monadic Boolean algebras, Compositio Math. 12 (1956), 217–249. MR 78304
  • P. R. Halmos, Algebraic logic. II. Homogeneous locally finite polyadic Boolean algebras of infinite degree, Fund. Math. 43 (1956), 255–325. MR 86029
  • L. Henkin, D. Monk and A. Tarski, Cylindric algebras, North-Holland, Amsterdam, 1971.
  • Bjarni Jónsson and Alfred Tarski, Boolean algebras with operators. I, Amer. J. Math. 73 (1951), 891–939. MR 44502, DOI 10.2307/2372123
  • P.-F. Jurie, Notion de quasi-somme amalgamée: Premières applications à I’algèbre boolérienne polyadique, C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A1033-A1036. MR 37 #3975.
  • Léon LeBlanc, Transformation algebras, Canadian J. Math. 13 (1961), 602–613. MR 132011, DOI 10.4153/CJM-1961-049-1
  • Anne Preller, Substitution algebras in their relation to cylindric algebras, Arch. Math. Logik Grundlag. 13 (1970), 91–96. MR 285369, DOI 10.1007/BF01967654
  • H. Rasiowa and R. Sikorski, A proof of the completeness theorem of Gödel, Fund. Math. 37 (1950), 193–200. MR 40232, DOI 10.4064/fm-37-1-193-200
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 02J15
  • Retrieve articles in all journals with MSC: 02J15
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 167-179
  • MSC: Primary 02J15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0317931-1
  • MathSciNet review: 0317931