The Cantor-Bernstein theorem was extended to a-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 a-complete MV-algebras, and compare it to a related result proved by Jakubik for certain complete MV-algebras.
A Cantor Bernstein theorem for sigma-complete MV-algebras / D.Mundici; A.De Simone; M.Navara. - In: CZECHOSLOVAK MATHEMATICAL JOURNAL. - ISSN 0011-4642. - STAMPA. - 53:(2003), pp. 437-447. [10.1023/A:1026299723322]
A Cantor Bernstein theorem for sigma-complete MV-algebras
MUNDICI, DANIELE;
2003
Abstract
The Cantor-Bernstein theorem was extended to a-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 a-complete MV-algebras, and compare it to a related result proved by Jakubik for certain complete MV-algebras.
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