The order type of the collection of finite series-parallel posets Original Research Article

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 Γ0 (J. Symbolic Logic 33 (1968) 193). Finite series-parallel posets form an age in Fraı̈sséʹs sense; we deduce that the height of N in the collection of its subages is also equal to Γ0.