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Zbl 1024.06003
De Simone, A.; Mundici, D.; Navara, M.
A Cantor-Bernstein theorem for $\sigma $-complete MV-algebras. (English)
[J] Czech. Math. J. 53, No.2, 437-447 (2003). ISSN 0011-4642; ISSN 1572-9141/e

Summary: The Cantor-Bernstein theorem was extended to $\sigma $-complete Boolean algebras by R. Sikorski and A. Tarski. Chang's MV-algebras are a nontrivial generalization of Boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as Boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to $\sigma $-complete MV-algebras, and compare it to a related result proved by J. Jakubík for certain complete MV-algebras.

MSC 2000:: *06D35 MV-algebras
03G20 Post and Lukasiewicz algebras (algebraic logic)

Keywords: Cantor-Bernstein theorem; MV-algebra; Boolean element; partition of unity; direct product decomposition; $\sigma $-complete MV-algebra

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