Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-18T11:41:18.528Z Has data issue: false hasContentIssue false

Certain Values of Completeness and Saturatedness of a Uniform Ideal Rule out Certain Sizes of The Underlying Index Set

Published online by Cambridge University Press:  20 November 2018

Frantisek Franek*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canadam5S 1A1 Department of Mathematics and Computer Science, Dartmouth College, Hanover, New Hampshire, USA03755
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the method of non-well-founded generic ultra-powers, we shall prove a generalization of a theorem of Taylor that certain values of completeness and saturatedness of a uniform ideal rule out certain sizes of the underlying index set.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Franek, F., Some results about saturated ideals and about isomorphisms of ĸ-trees, Ph.D. thesis, University of Toronto, 1983.Google Scholar
2. Jech, T., Set Theory, Academic Press, 1978.Google Scholar
3. Jech, T. and Prikry, K., Ideals over uncountable sets: applications of almost disjoint functions and generic ultrapowers, Mem. Amer. Math. Soc. 18 (1979), no. 214.Google Scholar
4. Solovay, R.M., Real-valued measurable cardinals, Axiomatic Set Theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, California, 1967), pp. 397428.Google Scholar
5. Silver, J., On the singular cardinals problem, Proceedings of the International Congress of Mathematicians (Vancouver, BC, 1974), Vol. I, pp. 265268.Google Scholar
6. Ulam, S., Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930).Google Scholar