Decidability and generation of the variety of distributive $\ell$-pregroups.

Abstract: Lattice-ordered pregroups ($\ell$-pregroups) represent a natural generalization of lattice ordered groups ($\ell$-groups). It is well-established that every $\ell$-group can be embedded into a symmetric one, as demonstrated by Cayley-Holland’s embedding theorem. Analogously, a Cayley-Holland’s embedding theorem exists for distributive $\ell$-pregroups, asserting that any distributive $\ell$-pregroup can be embedded into a functional one. In this work, we enhance this result by establishing that any distributive $\ell$-pregroup can be embedded into a functional one over a chain that is locally isomorphic to $\mathbb{Z}$. Utilizing this, we demonstrate that the variety of distributive $\ell$-pregroups is generated by the (single) functional algebra over the integers. We will later use this to prove the decidability of the variety.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic