The logic L*

SAGASTUME MARTA SUSANA; SAN MARTÍN HERNÁN JAVIER

MATHEMATICAL LOGIC QUARTERLY

WILEY-V C H VERLAG GMBH

Lugar: Weinheim; Año: 2014 vol. 60 p. 375 - 388

0942-5616

The algebraic category MV{bullet} is the image of MV, the category whose objects are MV-algebras, by the equivalence given in [1]. In this paper we define the logic L* whose Lindenbaum algebra is an MV{bullet}-algebra (object of MV{bullet}), and establish a link between L* and the infinite valued Lukasiewicz logic L. We define cU-operators, that have properties of universal quantifiers, and establish a bijection that maps an MV-algebra endowed with a U-operator into an MV{bullet}-algebra endowed with a c-U-operator. This map extends to a functor that is a categorical equivalence. References [1] J.L. Castiglioni, R. Lewin and M. Sagastume, On a definition of a variety of monadic l-groups (to appear in Studia Logica).