Mathematical Logic Quarterly 51 (6):570-578 (2005)

Given a π -institution I , a hierarchy of π -institutions I is constructed, for n ≥ 1. We call I the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I of I is also called the “Gentzenization” of I . In the main result of the paper, it is shown that I is strongly Gentzen , i.e. it is deductively equivalent to its Gentzenization via a special deductive equivalence, if and only if it has the deduction-detachment property
Keywords category of theories  Leibniz operator  equivalent institutions  Algebraic logic  metalogical properties  algebraizable logics  Gentzen institutions  lattice of theories  algebraizable institutions  equivalent deductive systems  Gentzen systems  deduction‐detachment theorem
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DOI 10.1002/malq.200310132
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A Survey of Abstract Algebraic Logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Equivalential and Algebraizable Logics.Burghard Herrmann - 1996 - Studia Logica 57 (2-3):419 - 436.

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