Abstract
So far, we have looked at lattices as a special kind of posets. In this chapter, we focus on another important special kind of posets: well-founded sets and well-ordered sets. Well-founded sets are partially ordered sets with the additional property that it is possible to use induction to prove that all elements have a given property. Well-ordered sets are simply well-founded sets on which the order is total.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Back, RJ., von Wright, J. (1998). Well-founded Sets and Ordinals. In: Refinement Calculus. Graduate Texts in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1674-2_18
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1674-2_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98417-9
Online ISBN: 978-1-4612-1674-2
eBook Packages: Springer Book Archive