Partition calculus and cardinal invariants

We prove that the strong polarized relation ((theta)(omega)) -> ((theta)(omega))(2)(1,1), applied simultaneously for every theta is an element of [Nu(1), 2(N0))], is consistent with ZFC. Consequently, , ((inv)(omega)) -> ((inv)(omega))(2)(1,1) is consistent for every cardinal invariant of the continuum. Some results in this direction are generalized to higher cardinals. Nous prouvons que la relation polarisee forte ((theta)(omega)) -> ((theta)(omega))(2)(1,1), appliquee simultanement a chaque cardinal theta is an element of [Nu(1), 2(N0))], est en accord avec ZFC. Par consequent, la relation ((inv)(omega)) -> ((inv)(omega))(2)(1,1) est en accord avec ZFC pour chaque caracteristique sur le continu. Nous etudions plusieurs generalisations pour certains cardinaux eleves.