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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?

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

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?

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

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

(When) can we construct models of a consistent first order theory $T$ from its Lindenbaum algebra?

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

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?

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