On the weak Freese-Nation property of P(omega)

Continuing [6], [8] and [16], we study the consequences of the weak Freese- Nation property of (P(omega), subset of or equal to). Under this assumption , we prove that most of the known cardinal invariants including all of thos e appearing in Cichon's diagram take the same value as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences of superatomic Boolean algebras in a Cohen model. These results show that the weak Freese-Nation property of (P(omega ), subset of or equal to) captures many of the features of Cohen models and hence may be considered as a principle axiomatizing a good portion of the combinatorics available in Cohen models.