We present the basic theory of the most natural algebraic counterpart of the ℵ0-valued Lukasiewicz calculus, strictly logically formulated. After showing its lattice structure and its relation to C. C. Chang's MV-algebras we study the implicative filters and prove its equivalence to congruence relations. We present some properties of the variety of all Wajsberg algebras, among which there is a representation theorem. Finally we give some characterizations of linear, simple and semisimple algebras.
@article{urn:eudml:doc:38902,
title = {Wajsberg algebras.},
journal = {Stochastica},
volume = {8},
year = {1984},
pages = {5-31},
zbl = {0557.03040},
mrnumber = {MR0780136},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38902}
}
Font, Josep M.; Rodríguez, Antonio J.; Torrens, Antoni. Wajsberg algebras.. Stochastica, Tome 8 (1984) pp. 5-31. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38902/