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

  • Authors:

  • Maurice Pouzet;Mohamed Sobrani

  • Affiliations:

  • Mathématiques, Université Claude-Bernard, 43, Bd. du 11 Novembre 1918, 69622 Villeurbanne, France;Mathématiques, Université de Fez, Faculté des Sciences et Techniques, B.P. 2202, Saïss-Fez, Morocco

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2003

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Abstract

It is well known that the collection N of finite series-parallel posets is well-quasiordered 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 Fraïssé's sense; we deduce that the height of N in the collection of its subages is also equal to Γ0.