Uniqueness problem with truncated multiplicities in value distribution theory

In 1929, H. Cartan declared that there are at most two meromorphic functions on C which share four values without multiplicities, which is incorrect but affirmative if they share four values counted with multiplicities truncated by two. In this paper, we generalize such a restricted H. Cartan's declaration to the case of maps into PN(C). We show that there are at most two nondegenerate meromorphic maps of C-n into P-N(C) which share 3N + 1 hyperplanes in general position counted with multiplicities truncated by two. We also give some degeneracy theorems of meromorphic maps into P-N(C) and discuss some other related subjects.