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Amalgamation through quantifier elimination for varieties of commutative residuated lattices

Amalgamation through quantifier elimination for varieties of commutative residuated lattices
Amalgamation through quantifier elimination for varieties of commutative residuated lattices
This work presents a model-theoretic approach to the study of the amalgamation property for varieties of semilinear commutative residuated lattices. It is well-known that if a first-order theory T enjoys quantifier elimination in some language L, the class of models of the set of its universal consequences T ∀ has the amalgamation property. Let Th(K) be the theory of an elementary subclass K of the linearly ordered members of a variety V of semilinear commutative residuated lattices. We show that whenever Th(K) has elimination of quantifiers, and every linearly ordered structure in V is a model of Th ∀(K), then V has the amalgamation property. We exploit this fact to provide a purely model-theoretic proof of amalgamation for particular varieties of semilinear commutative residuated lattices. © 2011 Springer-Verlag.
Amalgamation property, Quantifier elimination, Residuated lattices
0933-5846
15-34
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Marchioni, Enrico (2012) Amalgamation through quantifier elimination for varieties of commutative residuated lattices. Archive for Mathematical Logic, 51 (1-2), 15-34. (doi:10.1007/s00153-011-0251-x).

Record type: Article

Abstract

This work presents a model-theoretic approach to the study of the amalgamation property for varieties of semilinear commutative residuated lattices. It is well-known that if a first-order theory T enjoys quantifier elimination in some language L, the class of models of the set of its universal consequences T ∀ has the amalgamation property. Let Th(K) be the theory of an elementary subclass K of the linearly ordered members of a variety V of semilinear commutative residuated lattices. We show that whenever Th(K) has elimination of quantifiers, and every linearly ordered structure in V is a model of Th ∀(K), then V has the amalgamation property. We exploit this fact to provide a purely model-theoretic proof of amalgamation for particular varieties of semilinear commutative residuated lattices. © 2011 Springer-Verlag.

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e-pub ahead of print date: 20 December 2011
Published date: February 2012
Keywords: Amalgamation property, Quantifier elimination, Residuated lattices

Identifiers

Local EPrints ID: 416596
URI: http://eprints.soton.ac.uk/id/eprint/416596
ISSN: 0933-5846
PURE UUID: c1fe9602-5ab6-429e-a59b-efec8db51899

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Date deposited: 03 Jan 2018 17:30
Last modified: 13 Mar 2019 19:04

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Author: Enrico Marchioni

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