Abstract
In this paper we study Armstrong systems on ordered sets, and especially on complete join-semilattices. The set of all Armstrong systems on an ordered set P can be ordered with the usual set inclusion relation. We show that this ordered set is a complete lattice whenever P is a complete join-semilattice. We introduce dense sets of an Armstrong system and present some results concerning them. In particular, we characterize keys of a database relation in terms of dense sets.
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© 2001 Springer-Verlag London Limited
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Järvinen, J. (2001). Armstrong Systems on Ordered Sets. In: Calude, C.S., Dinneen, M.J., Sburlan, S. (eds) Combinatorics, Computability and Logic. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0717-0_12
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DOI: https://doi.org/10.1007/978-1-4471-0717-0_12
Publisher Name: Springer, London
Print ISBN: 978-1-85233-526-7
Online ISBN: 978-1-4471-0717-0
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