Varieties of Commutative Integral Bounded Residuated Lattices Admitting a Boolean Retraction Term

@article{Cignoli2012VarietiesOC,
  title={Varieties of Commutative Integral Bounded Residuated Lattices Admitting a Boolean Retraction Term},
  author={Roberto Cignoli and Antoni Torrens Torrell},
  journal={Studia Logica},
  year={2012},
  volume={100},
  pages={1107-1136}
}
Let BRL denote the variety of commutative integral bounded residuated lattices (bounded residuated lattices for short). A Boolean retraction term for a subvariety V of BRL is a unary term t in the language of bounded residuated lattices such that for every A ∈ V, t, the interpretation of the term on A, defines a retraction from A onto its Boolean skeleton B(A). It is shown that Boolean retraction terms are equationally definable, in the sense that there is a variety Vt BRL such that a variety V… CONTINUE READING