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Tytuł artykułu

On some properties of quasi MV algebras and square root quasi MV algebras. Part III

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In the present paper, which is a sequel to [14] and [3], we investigate further the structure theory of quasi-MV algebras and square root' 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�Lonsson�fs lemma, again for both varieties; we simplify the proof of standard completeness for the variety of square root ' quasi-MV algebras; we show that this same va- riety has the finite embeddability property; finally, we investigate the structure of the lattice of subvarieties of Square root' quasi-MV algebras.
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Tom
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161--199
Opis fizyczny
Bibliogr. 15 poz.
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Bibliografia
  • [1] W.J. Blok and I.M.A. Ferreirim, On the structure of hoops, Algebra Universalis 43(2000), pp. 233–257.
  • [2] W.J. Blok and C.J. van Alten, The finite embeddability property for residuated lattices, pocrims and BCK algebras, Algebra Universalis 48 (2002), pp. 253–271.
  • [3] F. Bou, F. Paoli, A. Ledda and H. Freytes, On some properties of quasi-MV algebras and p′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.
  • [5] I. Chajda, Jónsson’s Lemma for normally presented varieties, Mathematica Bohemica 122, 4 (1997), pp. 381–382.
  • [6] R. Cignoli, I.M.L. D’Ottaviano and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Kluwer, Dordrecht, 1999.
  • [7] I.M.A. Ferreirim, On Varieties and Quasivarieties of Hoops and Their Reducts, PhD Thesis, University of Chicago, 1992.
  • [8] R. Freese and R. McKenzie, Commutator Theory for Congruence Modular Varieties, London Mathematical Society Lecture Notes, vol. 125, Cambridge University Press,Cambridge, 1987.
  • [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 p′quasi-MV algebras, Journal of Logic and Computation, forthcoming.
  • [11] H.P. Gumm and A. Ursini, Ideals in universal algebras, Algebra Universalis 19 (1984), pp. 45–55.
  • [12] A. Ledda, M. Konig, F. Paoli and R. Giuntini, MV algebras and quantum computation, Studia Logica 82, 2 (2006), pp. 245–270.
  • [13] R. Lewin, M. Sagastume, P. Massey, MV* algebras, Logic Journal of the IGPL 12,6 (2004), pp. 461–483.
  • [14] F. Paoli, A. Ledda, R. Giuntini and H. Freytes, On some properties of quasi-MV algebras and p′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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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ5-0027-0063
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