Abstract
In this section we introduce two ideas important for the work to follow. The first of these is relational closure. In later sections we will be especially interested in sets that are transitive. While there exist sets that are not transitive every set has a transitive extension. Indeed, every set has a smallest transitive extension which we call its transitive closure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1971 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Takeuti, G., Zaring, W.M. (1971). Relational Closure and the Rank Function. In: Introduction to Axiomatic Set Theory. Graduate Texts in Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9915-5_9
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9915-5_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-05302-8
Online ISBN: 978-1-4684-9915-5
eBook Packages: Springer Book Archive