The Poset of All Logics I: Interpretations and Lattice Structure

Journal of Symbolic Logic 86 (3):935-964 (2021)
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Abstract

A notion of interpretation between arbitrary logics is introduced, and the poset$\mathsf {Log}$of all logics ordered under interpretability is studied. It is shown that in$\mathsf {Log}$infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between$\mathsf {Log}$and the lattice of interpretability types of varieties are investigated.

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Author's Profile

Ramon Jansana Ferrer
Universitat de Barcelona

Citations of this work

On Equational Completeness Theorems.Tommaso Moraschini - 2022 - Journal of Symbolic Logic 87 (4):1522-1575.

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References found in this work

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Reduced products of logical matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.

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