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Two theorems on the generation of systems of functions

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Selecta Mathematica

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Abstract

This paper deals with two basic questions about multiplace functions (“functions of several variables”) defined on a finite set Nm = {1, ..., m}. How many functions can k functions generate by composition, and how many functions are needed to generate by composition all p-place functions?

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References

  1. N. M. Martin, The Sheffer functions of the 3-valved logic J. Symb. Logic 19 (1954), pp. 45–51.

    Article  Google Scholar 

  2. K. Menger, Algebra of functions: past, present, future, Rend. Math. Roma 20 (1961), pp. 409–430.

    MathSciNet  MATH  Google Scholar 

  3. K. Menger, Superassociative systems and logical fweclors Math. Annalen 157 (1964), pp. 278–295.

    Article  MathSciNet  Google Scholar 

  4. S. Piccard, Sur les fonctions définies duns lea ensembles finis quelconques, Fund. Math. 24 (1935), pp. 298–301.

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  5. E. L. Post, Introduction to a general Theory of elementary propositions, Amer. J. Math. 43 (1921), pp. 163–185.

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  6. J. Slupecki, C. R. Soc. Sci. Let. Varsovie, Cl. III, 32 (1939).

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  7. H. I. Whitlock, A composition. algebra for multiplace functions Math. Annalen 157 (1964) pp. 167–178.

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Author information

Authors and Affiliations

  1. Chicago, USA

    Karl Menger & H. Ian Whitlock

Authors
  1. Karl Menger
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  2. H. Ian Whitlock
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Center, Amherst, MA, USA

    Bert Schweizer

  2. Department of Mathematics, Illinois Institute of Technology, Chicago, IL, USA

    Abe Sklar

  3. Institute of Mathematics, University of Vienna, Austria

    Karl Sigmund  & Leopold Schmetterer  & 

  4. Institute of Analysis and Technical Mathematics, Technical University, Vienna, Austria

    Peter Gruber  & Edmund Hlawka  & 

  5. Institute of Mathematics, University of Graz, Austria

    Ludwig Reich

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© 2003 Springer-Verlag Wien

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Menger, K., Whitlock, H.I. (2003). Two theorems on the generation of systems of functions. In: Schweizer, B., et al. Selecta Mathematica. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6045-9_26

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  • DOI: https://doi.org/10.1007/978-3-7091-6045-9_26

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  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7294-0

  • Online ISBN: 978-3-7091-6045-9

  • eBook Packages: Springer Book Archive

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