Set Theory and Arithmetic in Fuzzy Logic

Authors: Libor Běhounek, Zuzana Haniková
Publication year: 2015
Publication type: Kapitola v monografii
Periodical: Petr Hájek on Mathematical Fuzzy Logic
Projects: Logic-based fuzzy mathematics
Mathematical Fuzzy Logic in Computer Science
Bibliographic citation: BĚHOUNEK, Libor, HANIKOVÁ, Zuzana. Set Theory and Arithmetic in Fuzzy Logic. In: MONTAGNA, F., ed. Petr Hájek on Mathematical Fuzzy Logic. Cham: Springer, 2015, S. 63-89. Outstanding Contributions to Logic, 6. ISBN 978-3-319-06232-7
Dostupné z: doi:10.1007/978-3-319-06233-4_4
DOI: 10.1007/978-3-319-06233-4_4
ID: 432931

Abstract

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.