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On a homogeneity condition for MV-algebras. (English) Zbl 1164.06314

Summary: In this paper we deal with a homogeneity condition for an MV-algebra concerning a generalized cardinal property. As an application, we consider the homogeneity with respect to \(\alpha \)-completeness, where \(\alpha \) runs over the class of all infinite cardinals.

MSC:

06D35 MV-algebras
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References:

[1] S. J. Bernau: Lateral and Dedekind completion of archimedean lattice groups. J. London Math. Soc. 12 (1976), 320–322. · Zbl 0333.06008
[2] R. Cignoli, I. M. I. D’Ottaviano, and D. Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers, Dordrecht, 2000. · Zbl 0937.06009
[3] P. F. Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444–480. · Zbl 0182.04803
[4] A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers and Ister Science, Dordrecht and Bratislava, 2000.
[5] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. · Zbl 0259.06015
[6] J. Jakubík: Orthogonal hull of a strongly projectable lattice ordered group. Czechoslovak Math. J. 28 (1978), 484–504. · Zbl 0391.06014
[7] J. Jakubík: Direct product decompositions of MV-algebras. Czechoslovak Math. J. 44 (1994), 725–739. · Zbl 0821.06011
[8] J. Jakubík: On complete MV-algebras. Czechoslovak Math. J. 45 (1995), 473–480. · Zbl 0841.06010
[9] J. Jakubík: On archimedean MV-algebras. Czechoslovak Math. J. 48 (1998), 575–582. · Zbl 0951.06011
[10] J. Jakubík: Retract mappings of projectable MV-algebras. Soft Computing 4 (2000), 27–32. · Zbl 1005.06007
[11] J. Jakubík: Direct product decompositions of pseudo MV-algebras. Archivum Math. 37 (2001), 131–142. · Zbl 1070.06003
[12] J. Jakubík: On the {\(\alpha\)}-completeness of pseudo MV-algebras. Math. Slovaca 52 (2002), 511–516. · Zbl 1030.06009
[13] J. Jakubík: Generalized cardinal properties of lattices and lattice ordered groups. Czechoslovak Math. J 54 (2004), 1035–1053. · Zbl 1080.06029
[14] R. S. Pierce: Some questions about complete Boolean-algebras. Proc. Sympos. Pure Math. 2 (1961), 129–140. · Zbl 0101.27104
[15] E. C. Weinberg: Higher degrees of distributivity in lattices of continuous functions. Trans. Amer. Math. Soc. 104 (1962), 334–346. · Zbl 0105.09401
[16] W. A. Luxemburg, A. C. Zaanen: Riesz Spaces, Vol. 1. North Holland, Amsterdam, 1971.
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