A Cantor-Bernstein Theorem for σ-Complete MV-Algebras


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Abstract

The Cantor-Bernstein theorem was extended to σ-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 Lukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to σ-complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.

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