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On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV

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Jipsen P., Ledda A., Paoli F.

Reports on Mathematical Logic

2013

vol. 48

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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1 Reports on Mathematical Logic

1 2013

1 Jipsen P.

1 Ledda A.

1 Paoli F.

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On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV