Conference abstracts

Session S09 - Logic and Universal Algebra

July 26, 17:30 ~ 18:20

## Stonean residuated lattices

### Roberto Cignoli

### Universidad de Buenos Aires, Argentina - cignoli@dm.uba.ar

By a Stonean residuated lattice I mean a bounded integral residuated lattice-ordered commutative monoid satisfying the equation $$\neg x \lor \neg\neg x = \top.$$ I will show that stonean residuated lattices are characterized by triples $\langle \mathbf{B}, \mathbf{D}, \varphi\rangle$ where $\mathbf{B}$ is a Boolean algebra, $\mathbf{D}$ is an unbounded residuated lattice and $\varphi$ is an order reversing homomorphism from $\mathbf{B}$ into the lattice of implicative filters of $\mathbf{D}$.

Joint work with Manuela Busaniche (Universidad Nacional del Litoral, Argentina).