The order type of the collection of finite series-parallel posets

It is well known that the collection N of finite series-parallel posets is well-quasi-ordered under embeddability. Here, we show that the ordinal length of N, that is the maximum of the order types of its linear extensions, is the Feferman ordinal Gamma(0) (J. Symbolic Logic 33 (1968) 193). Finite series-parallel posets form an age in Fraisse's sense; we deduce that the height of N in the collection of its subages is also equal to Gamma(0). (C) 2002 Published by Elsevier Science B.V.