Subrecursive Complexity of Identifying the Ramsey Structure of Posets

  • Willem L. Fouché
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)

Abstract

We show that finite ordinal sums of finite antichains are Ramsey objects in the category of finite posets and height-preserving embeddings. Our proof yields a primitive recursive algorithm for constructing the finite posets which contain the required homogeneities. We also find, in terms of the classical Ramsey numbers, best possible upper bounds for the heights of the posets in which the homogeneous structures can be found.

Keywords

subrecursive hierarchy partially ordered sets (posets) structural Ramsey theory 

Mathematics Subject Classification (2000)

03D20 68Q17 06A07 05D10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Willem L. Fouché
    • 1
  1. 1.Department of Decision SciencesUniversity of South AfricaPretoriaSouth Africa

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