On Order-Perfect Lattices

Igor Kříž ()
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Igor Kříž: The University of Michigan, Department of Mathematics

A chapter in The Mathematics of Paul Erdős II, 2013, pp 427-439 from Springer

Abstract: Summary We investigate the property of certain well-founded orderings to have a chain of maximal ordinal length. We show that Heyting algebras and countable modular lattices have this property, but we also present an example of a “well-behaved” lattice which does not have it. We prove a general necessary and sufficient condition for modular lattices to have the property in a hereditary form. This hereditary form is called order-perfectness, being analogous to perfectness of finite graphs. Certain well-known theorems of D.H.J. de Jongh, R. Parikh, D. Schmidt, E.C. Milner, N. Sauer, and N. Zaguia turn out to be order-perfectness results.

Keywords: Modular Lattice; Heyting Algebra; Ordinary Length; Hereditary Forms; Well-founded Ordering (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7254-4_25

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DOI: 10.1007/978-1-4614-7254-4_25

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