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A Cantor-Bernstein theorem for \(\sigma \)-complete MV-algebras. (English) Zbl 1024.06003
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:
06D35 MV-algebras
03G20 Logical aspects of Łukasiewicz and Post algebras
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References:
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