Ordinal decompositions for preordered root systems

In this paper, we explore the effects of certain forbidden substructure conditions on preordered sets. In particular, we characterize in terms of these conditions those preordered sets which can be represented as the supremum of a well-ordered ascending chain of lowersets whose members are construct...

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Bibliographic Details
Published in:Annals of pure and applied logic 2009-11, Vol.161 (2), p.203-211
Main Authors: Hart, James B., Tsinakis, Constantine
Format: Article
Language:English
Subjects:
Denotational semantics
Information systems
Ordinal decomposition
Ordinal extension
Partially ordered sets
Preordered sets
Root system
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Summary:In this paper, we explore the effects of certain forbidden substructure conditions on preordered sets. In particular, we characterize in terms of these conditions those preordered sets which can be represented as the supremum of a well-ordered ascending chain of lowersets whose members are constructed by means of alternating applications of disjoint union and ordinal sums with chains. These decompositions are examples of ordinal decompositions in relatively normal lattices as introduced by Snodgrass, Tsinakis, and Hart. We conclude the paper with an application to information systems.
ISSN:0168-0072
DOI:10.1016/j.apal.2009.05.004