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Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with substitutions. We show that the π-institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-F´erez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-F´erez pertaining to arbitrary multi-term π-institutions. The approach places hidden multi-sorted deductive systems in a more general framework and bypasses the laborious reuse of well-known proof techniques from traditional abstract algebraic logic by using “off the shelf” tools.
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2016-06-30
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bwmeta1.element.ojs-doi-10_18778_0138-0680_45_2_04