On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
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RIS BIB ENDNOTEOn some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
Publication date: 26.11.2013
Reports on Mathematical Logic, 2013, Number 48, pp. 3-36
https://doi.org/10.4467/20842589RM.13.001.1201Authors
On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
In the present paper, which is a sequel to [20, 4, 12], we investigate further the structure theory of quasi-MV algebras and √ quasi-MV algebras. In particular: we provide a new representation of arbitrary √ qMV algebras in terms of √ qMV algebras arising out of their MV* term subreducts of regular elements; we investigate in greater detail the structure of the lattice of √ qMV varieties, proving that it is uncountable, providing equational bases for some of its members, as well as analysing a number of slices of special interest; we show that the variety of √ qMV algebras has the amalgamation property; we provide an axiomatisation of the 1-assertional logic of √ qMV algebras; lastly, we reconsider the correspondence between Cartesian √ qMV algebras and a category of Abelian lattice-ordered groups with operators first addressed in [10].
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Information: Reports on Mathematical Logic, 2013, Number 48, pp. 3-36
Article type: Original article
Department of Mathematics, Chapman University, USA
Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy
Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy
Published at: 26.11.2013
Article status: Open
Licence: None
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