Abstract
It is shown that the class of reduced matrices of a logic ⊢ is a 1st order ∀∃-class provided the variety associated with ⊢ has the finite replacement property in the sense of [7]. This applies in particular to all 2-valued logics. For 3-valued logics the class of reduced matrices need not be 1st order.
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Rautenberg, W. On reduced matrices. Stud Logica 52, 63–72 (1993). https://doi.org/10.1007/BF01053064
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DOI: https://doi.org/10.1007/BF01053064