Some variations on the partition property for normal ultrafilters on Pkl
Barbanel, Julius
Fundamenta Mathematicae, Tome 142 (1993), p. 163-171 / Harvested from The Polish Digital Mathematics Library
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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 Pκλ. 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.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:211979 
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Barbanel, Julius. Some variations on the partition property for normal ultrafilters on Pkl. Fundamenta Mathematicae, Tome 142 (1993) pp. 163-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p163bwm/

[00000] [1] J. B. Barbanel, Supercompact cardinals and trees of normal ultrafilters, J. Symbolic Logic 47 (1982), 89-109. | Zbl 0503.03025

[00001] [2] J. B. Barbanel, Supercompact cardinals, trees of normal ultrafilters, and the partition property, ibid. 51 (1986), 701-708. | Zbl 0623.03051

[00002] [3] J. B. Barbanel, On the relationship between the partition property and the weak partition property for normal ultrafilters on Pκλ, ibid., to appear.

[00003] [4] K. Kunen, Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript, 1971.

[00004] [5] 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. | Zbl 0548.03031

[00005] [6] T. Menas, A combinatorial property of Pκλ, ibid. 41 (1976), 225-234.

[00006] [7] 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. | Zbl 0317.02083

[00007] [8] R. Solovay, W. Reinhardt, and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116. | Zbl 0376.02055