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A Cantor-Bernstein theorem for $\sigma$-complete MV-algebras
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 437-447
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The Cantor-Bernstein theorem was extended to $\sigma $-complete boolean algebras by Sikorski and 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 Jakubík for certain complete MV-algebras.
The Cantor-Bernstein theorem was extended to $\sigma $-complete boolean algebras by Sikorski and 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 Jakubík for certain complete MV-algebras.
Classification : 03G20, 06C15, 06D30, 06D35
Keywords: Cantor-Bernstein theorem; MV-algebra; boolean element of an MV-algebra; partition of unity; direct product decomposition; $\sigma $-complete MV-algebra 
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de Simone, A.; Mundici, D.; Navara, M. A Cantor-Bernstein theorem for $\sigma$-complete MV-algebras. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 437-447. http://geodesic.mathdoc.fr/item/CMJ_2003_53_2_a17/

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