# A Cantor-Bernstein theorem for $\sigma $-complete MV-algebras

Anna de Simone; Daniele Mundici; Mirko Navara

Czechoslovak Mathematical Journal (2003)

- Volume: 53, Issue: 2, page 437-447
- ISSN: 0011-4642

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topde Simone, Anna, Mundici, Daniele, and Navara, Mirko. "A Cantor-Bernstein theorem for $\sigma $-complete MV-algebras." Czechoslovak Mathematical Journal 53.2 (2003): 437-447. <http://eudml.org/doc/30789>.

@article{deSimone2003,

abstract = {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.},

author = {de Simone, Anna, Mundici, Daniele, Navara, Mirko},

journal = {Czechoslovak Mathematical Journal},

keywords = {Cantor-Bernstein theorem; MV-algebra; boolean element of an MV-algebra; partition of unity; direct product decomposition; $\sigma $-complete MV-algebra; Cantor-Bernstein theorem; MV-algebra; Boolean element; partition of unity; direct product decomposition; -complete MV-algebra},

language = {eng},

number = {2},

pages = {437-447},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A Cantor-Bernstein theorem for $\sigma $-complete MV-algebras},

url = {http://eudml.org/doc/30789},

volume = {53},

year = {2003},

}

TY - JOUR

AU - de Simone, Anna

AU - Mundici, Daniele

AU - Navara, Mirko

TI - A Cantor-Bernstein theorem for $\sigma $-complete MV-algebras

JO - Czechoslovak Mathematical Journal

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 53

IS - 2

SP - 437

EP - 447

AB - 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.

LA - eng

KW - Cantor-Bernstein theorem; MV-algebra; boolean element of an MV-algebra; partition of unity; direct product decomposition; $\sigma $-complete MV-algebra; Cantor-Bernstein theorem; MV-algebra; Boolean element; partition of unity; direct product decomposition; -complete MV-algebra

UR - http://eudml.org/doc/30789

ER -

## References

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## Citations in EuDML Documents

top- Hector Freytes, An algebraic version of the Cantor-Bernstein-Schröder theorem
- Anna De Simone, Mirko Navara, On the permanence properties of interval homogeneous orthomodular lattices
- Štefan Černák, Eighty years of Professor Ján Jakubík
- Ján Jakubík, On the Schröder-Bernstein problem for Carathéodory vector lattices
- Ján Jakubík, Isomorphisms of direct products of lattice-ordered groups
- Ján Jakubík, On a theorem of Cantor-Bernstein type for algebras

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