Geodesic
Descendingly Incomplete Ultrafilters and the Cardinality of Ultrapowers
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 830-834

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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|. 
Adler, Andrew; Jorgensen, Murray. Descendingly Incomplete Ultrafilters and the Cardinality of Ultrapowers. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 830-834. doi: 10.4153/CJM-1972-082-6
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[1] 1. Adler, A., The cardinality of ultrapowers—an example, Proc. Amer. Math. Soc. 28 (1971), 311–312. Google Scholar

[2] 2. Adler, A., Representation of models of full theories (to appear in Zeitschrift fur Grund. der Math.) Google Scholar

[3] 3. Chang, C. C., Descendingly incomplete ultrafilters, Trans. Amer. Math. Soc. 126 (1967), 108–111. Google Scholar

[4] 4. Keisler, H. J., On cardinalities of ultraproducts, Bull. Amer. Math. Soc. 70 (1964), 644–647. Google Scholar

[5] 5. Kunen, K., Two theorems on ultrafilters, Notices Amer. Math. Soc. 17 (1970), 673. Google Scholar

[6] 6. Kunen, K. and Prikry, K., On descendingly incomplete ultrafilters (to appear). Google Scholar

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