Sorry for this question out of the blue (especially if its answer should be trivial, obvious, or folklore):

> (When and how) can we construct models of a consistent
> first order theory $T$ from its
> [Lindenbaum algebra][1]?

More specifically: Is there an algebraic theory which its Lindenbaum algebra is a model of?





  [1]: https://en.wikipedia.org/wiki/Lindenbaum%E2%80%93Tarski_algebra