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Tree‐Properties for Ordered Sets
Author(s) -
Esser Olivier,
Hinnion Roland
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200202)48:2<213::aid-malq213>3.0.co;2-r
Subject(s) - mathematics , tree (set theory) , property (philosophy) , order (exchange) , combinatorics , pure mathematics , discrete mathematics , epistemology , philosophy , finance , economics
In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree‐property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ 0 ‐arborescent.