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Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas
Mathematical Logic Quarterly 53 (2):147-161 (2007)
Abstract
The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality-free first-order structures are provided in the framework of structure systems. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)Other Versions
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References found in this work
A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Some theorems on structural consequence operations.Stephen L. Bloom - 1975 - Studia Logica 34 (1):1 - 9.
Some characterization theorems for infinitary universal horn logic without equality.Pilar Dellunde & Ramon Jansana - 1996 - Journal of Symbolic Logic 61 (4):1242-1260.
On Elementary Equivalence for Equality-free Logic.E. Casanovas, P. Dellunde & R. Jansana - 1996 - Notre Dame Journal of Formal Logic 37 (3):506-522.
Categorical abstract algebraic logic: Equivalent institutions.George Voutsadakis - 2003 - Studia Logica 74 (1-2):275 - 311.
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