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Superassociative Systems and Logical Functors

  • Karl Menger
Chapter
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Abstract

Mathematicans often refer to our time as the age of algebra and of axiomatic theories. Paradoxically, however, the branch of mathematics which for three centuries has been at the very core of mathematics — analysis — has been neither ‘algebraicized’ nor axiomatized.

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References

  1. [1]
    Mannos, M.: Ideals in tri-operational algebra. Reports Math. Coll., 2nd series, Notre Dame 7, 73–79 (1946).MathSciNetGoogle Scholar
  2. [2]
    Mehlberg, J. J.: A classification of mathematical concepts. Synthese 14, 78–86 (1962).CrossRefGoogle Scholar
  3. [3]
    Menger, K.: A counterpart of Occam’s Razor in pure and applied mathematics. Synthese 12, 415–428 (1960) and 13, 331–349 (1961).CrossRefGoogle Scholar
  4. [4]
    Menger, K.: Gulliver in the land without One, Two, Three. Math. Gaz. 43, 241–250 (1959).MathSciNetCrossRefGoogle Scholar
  5. [5]
    Menger, K.: Gulliver’s return to the land without One, Two, Three. Am. Math. Monthly 67, 641–648 (1960).MathSciNetCrossRefGoogle Scholar
  6. [6]
    Menger, K.: Tri-operational algebra. Reports Math. Coll., 2nd ser., Notre Dame 5–6, 3–10 (1945).Google Scholar
  7. [7]
    Menger, K.: General algebra of analysis. Reports Math. Coll., 2nd ser., Notre Dame 7, 46–60 (1946).Google Scholar
  8. [8]
    Menger, K.: Algebra of analysis. Notre Dame Math. Lect. 3 (1944).Google Scholar
  9. [9]
    Menger, K.: Calculus. A Modern Approach. Boston: Ginn 1955.zbMATHGoogle Scholar
  10. [10]
    Menger, K.: An axiomatic theory of functions and fluents. In The Axiomatic Method, 454–473, ed. Henkin et al. Amsterdam: North-Holland Publ. Co. 1959.CrossRefGoogle Scholar
  11. [11]
    Menger, K.: Algebra of functions: past, present, future. Rend. Mat. Roma 20, 409–430 (1961).MathSciNetzbMATHGoogle Scholar
  12. [12]
    Menger, K.: Function algebra and propositional calculus. In Self-Organizing Systems 1962, 525–532. Ed. Yovits et al. Washington: Spartan Books.Google Scholar
  13. [13]
    Miloram, A. N.: Saturated polynomials. Reports Math. Coll., 2nd ser., Notre Dame 7, 65–68 (1946).Google Scholar
  14. [14]
    Nöbauer, W.: Über die Operation des Einsetzens in Polynomringen. Math. Ann. 134, 248–259 (1958) and Funktionen auf kommutativen Ringen. Math. Ann. 147, 166–175 (1962).MathSciNetCrossRefGoogle Scholar
  15. [15]
    Post, E.: The two-valued iterative systems of mathematical logic. Princeton Univ. Press (1941).Google Scholar
  16. [16]
    Schweizer, B., and A. Sklar: The algebra of functions. Math. Ann. 139, 366–382 (1960); 143, 440–447 (1961) and a forthcoming third paper.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Schweizer, B., and A. Sklar: A mapping algebra with infinitely many operations. Coll. Math. 9, 33–38 (1962).MathSciNetCrossRefGoogle Scholar
  18. [18]
    Seall, R. E.: Truth-valued fluents and qualitative laws. Philos. Sci. 30, 36–41 (1963).CrossRefGoogle Scholar
  19. [19]
    Whitlock, H. I.: A composition algebra for multiplace functions. Math. Ann. 157, 167–178 (1964).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • Karl Menger
    • 1
  1. 1.ChicagoUSA

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