  In this paper we first formulate several ``combinatorial principles''
concerning kappa \times omega matrices of subsets of omega and prove that they
are valid in the generic extension obtained by adding any number of Cohen reals
to any ground model V, provided that the parameter kappa is an
omega-inaccessible regular cardinal in V.
  Then we present a large number of applications of these principles, mainly to
topology. Some of these consequences had been established earlier in generic
extensions obtained by adding omega_2 Cohen reals to ground models satisfying
CH, mostly for the case kappa=omega_2.
