Free Monadic Three-valued Lukasiewicz Algebras

IGNACIO VIGLIZZO

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahía Blanca; Año: 1998 vol. 1998 p. 109 - 117

0041-6932

In this work the concept of free monadic extension of a three-valued Lukasiewicz algebra is defined and used to obtain the free monadic three-valued Lukasiewicz algebra with a finite set of free generators G up from the free three-valued Lukasiewicz algebra with the same set of free generators, following a method introduced by P. Halmos in [5]. This method also allows us to know the coordinates of the generators on each axis. As particular cases, free monadic boolean and three-valued Post algebras with a finite set of generators are determined, as well as the corresponding free monadic algebras over a given finite poset. P. Halmos´ technique has been used by R. Cignoli in the case of Q-distributive lattices [2] and by A. Petrovich in the case of monadic De Morgan algebras [15], of which the monadic three-valued Lukasiewicz algebras can be seen as a particular case.