Some variations on the partition property for normal ultrafilters on Pkl

Julius Barbanel

ArticleOriginal scientific text

Title

Some variations on the partition property for normal ultrafilters on Pkl

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Affiliations

Department of Mathematics, Union College Schenectady, New York 12308, U.S.A.

Abstract

Suppose κ is a supercompact cardinal and λ≥κ. In [3], we studied the relationship between the weak partition property and the partition property for normal ultrafilters on

P_{κ} λ

. In this paper we study a hierarchy of properties intermediate between the weak partition property and the partition property. Given appropriate large cardinal assumptions, we show that these properties are not all equivalent.

J. B. Barbanel, Supercompact cardinals and trees of normal ultrafilters, J. Symbolic Logic 47 (1982), 89-109.
J. B. Barbanel, Supercompact cardinals, trees of normal ultrafilters, and the partition property, ibid. 51 (1986), 701-708.
J. B. Barbanel, On the relationship between the partition property and the weak partition property for normal ultrafilters on $P_{κ} λ$ , ibid., to appear.
K. Kunen, Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript, 1971.
K. Kunen and D. H. Pelletier, On a combinatorial property of Menas related to the partition property for measures on supercompact cardinals, J. Symbolic Logic 48 (1983), 475-481.
T. Menas, A combinatorial property of $P_{κ} λ$ , ibid. 41 (1976), 225-234.
R. Solovay, Strongly compact cardinals and the GCH, in: Proceedings of the Tarski Symposium, L. Henkin et al. (eds.), Proc. Sympos. Pure Math. 25, Amer. Math. Soc., Providence, R.I., 1974, 365-372.
R. Solovay, W. Reinhardt, and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm142/fm14225.pdf

Title

Some variations on the partition property for normal ultrafilters on Pkl

Affiliations

Abstract

Bibliography

Additional information