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Some notes on elimination properties for the theory of Riesz MV-Chains

Some notes on elimination properties for the theory of Riesz MV-Chains
Some notes on elimination properties for the theory of Riesz MV-Chains
Riesz MV-algebras are a variety of algebras strongly connected to Riesz spaces. In this short article we investigate some elimination properties of the first-order theory RMV of linearly ordered Riesz MV-algebras and show that RMV admits elimination of quantifiers and uniform elimination of imaginary elements. In the process, we also prove several other results such as modelcompleteness, o-minimality, definability of Skolem functions, and a version of the Di Nola Representation Theorem for Riesz MV-algebras.
Riesz MV-algebras, elimination of imaginaries, quantifier elimination
0139-9918
789-800
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Marchioni, Enrico (2015) Some notes on elimination properties for the theory of Riesz MV-Chains. Mathematica Slovaca, 65 (4), 789-800. (doi:10.1515/ms-2015-0055).

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Abstract

Riesz MV-algebras are a variety of algebras strongly connected to Riesz spaces. In this short article we investigate some elimination properties of the first-order theory RMV of linearly ordered Riesz MV-algebras and show that RMV admits elimination of quantifiers and uniform elimination of imaginary elements. In the process, we also prove several other results such as modelcompleteness, o-minimality, definability of Skolem functions, and a version of the Di Nola Representation Theorem for Riesz MV-algebras.

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Published date: 1 August 2015
Keywords: Riesz MV-algebras, elimination of imaginaries, quantifier elimination

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Local EPrints ID: 416595
URI: http://eprints.soton.ac.uk/id/eprint/416595
ISSN: 0139-9918
PURE UUID: 9fa3e67b-a962-4d25-842f-1587a6cb7d32

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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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