Abstract

Let D be an ultrafilter on I, and let k be a cardinal. D is said to be k-descendingly incomplete (k-d.i.) if there exists a chain Xα : α < k of elements of D such that α < β → Xα ⊆ Xβ and Xα = ϕ. Such a chain will be called a k-chain for D. The notion of k-descending incompleteness is due to Chang [3].In this paper we explore the relationship between the cardinality of the ultrapower kI/D and the existence of certain chains on D. Since we deal so much with questions of size, we do not ordinarily make a notational distinction between a set and its cardinality. Where such a distinction is useful, the cardinality of a set A will be denoted by |A|.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.