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Some Remarks on Pseudotrees

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Abstract

This paper provides new results on pseudotrees. First, it is shown that pseudotrees are precisely those posets for which consistent sets, directed sets, and nonempty chains coincide. Second, we show that chain-complete pseudotrees yield complete meet-semilattices. Third, we prove that pseudotrees are precisely those posets that admit a set representation by sets of appropriate chains. This latter result generalizes results needed for applications in game theory and economics.

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Authors and Affiliations

  1. Department of Economics, University of Vienna, Hohenstaufengasse 9, 1010, Vienna, Austria

    Carlos Alós-Ferrer

  2. Department of Economics and Finance, Institute for Advanced Studies, Stumpergasse 56, 1060, Vienna, Austria

    Klaus Ritzberger

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  1. Carlos Alós-Ferrer
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  2. Klaus Ritzberger
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Correspondence to Carlos Alós-Ferrer.

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Alós-Ferrer, C., Ritzberger, K. Some Remarks on Pseudotrees. Order 22, 1–9 (2005). https://doi.org/10.1007/s11083-005-9001-1

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  • DOI: https://doi.org/10.1007/s11083-005-9001-1

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