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.
Amalgamation property, Quantifier elimination, Residuated lattices
15-34
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
February 2012
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), .
(doi:10.1007/s00153-011-0251-x).
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.
This record has no associated files available for download.
More information
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
Catalogue record
Date deposited: 03 Jan 2018 17:30
Last modified: 15 Mar 2024 17:37
Export record
Altmetrics
Contributors
Author:
Enrico Marchioni
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics