  According to Horrocks (1966), a vector bundle E on the projective n-space
extends stably to the projective N-space, N>n, if there exists a vector bundle
on the larger space whose restriction to the smaller one is isomorphic to E
plus a direct sum of line bundles. We show that E extends stably to the
projective N-space for every N>n if and only if E is the cohomology of a free
monad (with three terms). The proof uses the method of Coanda and Trautmann
(2006). Combining this result with a theorem of Mohan Kumar, Peterson and Rao
(2003), we get a new effective version of the Babylonian tower theorem for
vector bundles on projective spaces.
