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

Tomasz Kowalski

Titles

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

Abstract

In the present paper, which is a sequel to [14] and [3], we investigate further the structure theory of quasi-MV algebras and √′quasi-MV algebras. In particular: we provide an improved version of the subdirect representation theorem for both varieties; we characterise the Ursini ideals of quasi-MV algebras; we establish a restricted version of J´onsson’s lemma, again for both varieties; we simplify the proof of standard completeness for the variety of √′ quasi-MV algebras; we show that this same variety has the finite embeddability property; finally, we investigate the structure of the lattice of subvarieties of √′quasi-MV algebras.

References

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[3] F. Bou, F. Paoli, A. Ledda and H. Freytes, On some properties of quasi-MV algebras and √′quasi-MV algebras. Part II, Soft Computing 12, 4 (2008), pp. 341–352.

[4] F. Bou, F. Paoli, A. Ledda, M. Spinks and R. Giuntini, The logic of quasi-MV algebras, Journal of Logic and Computation, forthcoming.

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[9] R. Giuntini, A. Ledda and F. Paoli, Expanding quasi-MV algebras by a quantum operator, Studia Logica 87, 1 (2007), pp. 99–128. [10] R. Giuntini, A. Ledda and F. Paoli, Categorical equivalences for √′quasi-MV algebras, Journal of Logic and Computation, forthcoming.

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[12] A. Ledda, M. Konig, F. Paoli and R. Giuntini, MV algebras and quantum computation, Studia Logica 82, 2 (2006), pp. 245–270.

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[14] F. Paoli, A. Ledda, R. Giuntini and H. Freytes, On some properties of quasi-MV algebras and √′quasi-MV algebras. Part I, Reports on Mathematical Logic 44 (2008), pp. 53–85.

[15] A. Salibra, Topological incompleteness and order incompleteness in lambda calculus, ACM Transactions on Computational Logic 4, 3 (2003), pp. 379–401.

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Information: Reports on Mathematical Logic, 2010, Number 45, pp. 161 - 199

Article type: Original article

Titles:

Polish:

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

English:

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

Authors

Tomasz Kowalski

Published at: 20.09.2010

Article status: Open

Licence: None

Percentage share of authors:

Tomasz Kowalski (Author) - 100%

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