INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
congresos y reuniones científicas
Cantor-Bersntein-Schroder theorem and the congruences lattice of an algebra
Congreso; Logic Algebra and truth degrees first conferences of the working group on Mathematical fuzzy logic; 2008
Universita di Siena
The famous Cantor-Bernstein-Schr¨oder theorem (CBS theorem, for short) states that, if a set X can be embedded into a set Y and viceversa, then there is a one-to-one function from X onto Y . At the end of the forties, Sikorski (see also Tarski) showed that the CBS theorem is a particular case of a statement on sigma-complete boolean algebras. Recently several authors extended Sikorskis result to classes of algebras more general than boolean algebras, like orthomodular lattices, MV-algebras , pseudo MV-algebras , effect algebras, algebras with an underlying lattice structure etc. The aim of this work is to give a general algebraic frame for the validity of the CBS theorem, from which all the versions mentioned above can be derived. The abstract frame for the CBS theorem is given by the congruence lattice of an algebra. Moreover, necessary and sufficient conditions for the validity of the CBS theorem in algebras are given.