  We reduce the basis construction problem for Hopf algebras generated by
skew-primitive semi-invariants to a study of special elements, called
``super-letters,'' which are defined by Shirshov standard words. In this way we
show that above Hopf algebras always have sets of PBW-generators (``hard''
super-letters). It is shown also that these Hopf algebras having not more than
finitely many ``hard'' super-letters share some of the properties of universal
enveloping algebras of finite-dimensional Lie algebras. The background for the
proofs is the construction of a filtration such that the associated graded
algebra is obtained by iterating the skew polynomials construction, possibly
followed with factorization.
