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A duality theorem

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Summary

For a sufficiently large class of formal systems a duality theorem is proved.

We consider such formal set theoriesT [2] which, at least, satisfy the following conditions:

  1. 1.

    The theoryT contains its own (either bounded or introduced by a definition) substantive constantU, for which ⊢∀x[x∈U] or ⊢∀x[x⊂U].

  2. 2.

    The operation of “complement”, denoted byC, is defined with respect toU.

  3. 3.

    For any formula (resp. a term),A⊢A↔ℸℸA (resp. ⊢CCA=A), and some basic conclusions follow.

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References

  1. N. Bourbaki,Set Theory, (in Russian), Moscow 1965.

  2. Sh. S. Pkhakadze,On a class of abbreviating symbols, in:Studies in Mathematical Logic and Theory of Algorithms (in Russian), Tbilisi 1975.

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Authors and Affiliations

  1. Tbilisi State University, Tbilisi, USA

    Kh. M. Rukhaia

  2. Warsaw University, Warsaw, Poland

    Kh. M. Rukhaia

Authors
  1. Kh. M. Rukhaia
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Allatum est die 25 Julii 1976

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Rukhaia, K.M. A duality theorem. Stud Logica 37, 157–159 (1978). https://doi.org/10.1007/BF02124801

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  • DOI: https://doi.org/10.1007/BF02124801

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