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An algebraic characterization of o-minimal and weakly o-minimal MV-chains

An algebraic characterization of o-minimal and weakly o-minimal MV-chains
An algebraic characterization of o-minimal and weakly o-minimal MV-chains
We present an algebraic characterization of both o-minimal and weakly o-minimal MV-chains by showing that a linearly ordered MV-algebra is (1) o-minimal if and only if it is finite or divisible, and (2) weakly o-minimal if and only if its first-order theory admits quantifier elimination in the language 〈⊕, *, 0〉 if and only if Rad(A) is a divisible monoid and A/Rad(A) is either finite or divisible. © 2013 Elsevier B.V.
0022-4049
90-100
Lenzi, Giacomo
fd780e56-7ded-42f2-af80-8a2d076c78d3
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Lenzi, Giacomo
fd780e56-7ded-42f2-af80-8a2d076c78d3
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Lenzi, Giacomo and Marchioni, Enrico (2014) An algebraic characterization of o-minimal and weakly o-minimal MV-chains. Journal of Pure and Applied Algebra, 218 (1), 90-100. (doi:10.1016/j.jpaa.2013.04.014).

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Abstract

We present an algebraic characterization of both o-minimal and weakly o-minimal MV-chains by showing that a linearly ordered MV-algebra is (1) o-minimal if and only if it is finite or divisible, and (2) weakly o-minimal if and only if its first-order theory admits quantifier elimination in the language 〈⊕, *, 0〉 if and only if Rad(A) is a divisible monoid and A/Rad(A) is either finite or divisible. © 2013 Elsevier B.V.

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Lenzi Marchioni Algebraic Characterisation - Accepted Manuscript
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e-pub ahead of print date: 3 May 2013
Published date: January 2014

Identifiers

Local EPrints ID: 416592
URI: http://eprints.soton.ac.uk/id/eprint/416592
ISSN: 0022-4049
PURE UUID: 6eeab327-b8da-46d5-99dc-7ab7901f42c4

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Date deposited: 03 Jan 2018 17:30
Last modified: 25 Nov 2019 18:34

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Author: Giacomo Lenzi
Author: Enrico Marchioni

University divisions

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