Set Theory and Arithmetic in Fuzzy Logic

  • Libor BěhounekEmail author
  • Zuzana Haniková
Part of the Outstanding Contributions to Logic book series (OCTR, volume 6)


This chapter offers a review of Petr Hájek’s contributions to first-order axiomatic theories in fuzzy logic (in particular, ZF-style fuzzy set theories, arithmetic with a fuzzy truth predicate, and fuzzy set theory with unrestricted comprehension schema). Generalizations of Hájek’s results in these areas to MTL as the background logic are presented and discussed.


Fuzzy set theory Fuzzy logic Naive comprehension Non-classical arithmetic 



The work was supported by grants No. P103/10/P234 (L. Běhounek) and P202/10/1826 (Z. Haniková) of the Czech Science Foundation.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPragueCzech Republic
  2. 2.Institute for Research and Applications of Fuzzy ModelingNSC IT4Innovations, Division University of OstravaOstravaCzech Republic

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