Studia Logica

, Volume 39, Issue 4, pp 335–345 | Cite as

Set theory as modal logic

  • Herman Dishkant


A logical systemBM+ is proposed, which, is a prepositional calculus enlarged with prepositional quantifiers and with two modal signs, □ and Δ These modalities are submitted to a finite number of axioms. □ is the usual sign of necessity, Δ corresponds to transmutation of a property (to be white) into the abstract property (to be the whiteness). An imbeddingσ of the usual theory of classesM intoBM+ is constructed, such that a formulaA is provable inM if and only ifσ(A) is provable inBM+. There is also an inverse imbeddingπ with an analogous property.


Finite Number Mathematical Logic Modal Logic Modal Sign Computational Linguistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Tarski,Logic, Semantics, Metamathematics, Oxford, 1956.Google Scholar
  2. [2]
    K. Fine,Propositional quantifiers in modal logic,Theoria 36 (1970), pp. 336–346.Google Scholar
  3. [3]
    A. Morse,A theory of sets, Academic Press, N.-Y., 1965.Google Scholar
  4. [4]
    A. Mostowski,Constructible sets with applications, Amsterdam, 1969.Google Scholar

Copyright information

© Polish Academy of Sciences 1980

Authors and Affiliations

  • Herman Dishkant
    • 1
  1. 1.University of KalininUSSR

Personalised recommendations