Some variations on the partition property for normal ultrafilters on Pkl

• Autorzy: Julius B. Barbanel
• Języki publikacji: EN

Abstrakty

EN

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 $P_κλ$. 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 142
• Numer: 2
• Strony: 163-171

Daty

wydano

1993

otrzymano

1992-03-31

Twórcy

autor

Julius B. Barbanel

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

Bibliografia

• [1] J. B. Barbanel, Supercompact cardinals and trees of normal ultrafilters, J. Symbolic Logic 47 (1982), 89-109.
• [2] J. B. Barbanel, Supercompact cardinals, trees of normal ultrafilters, and the partition property, ibid. 51 (1986), 701-708.
• [3] J. B. Barbanel, On the relationship between the partition property and the weak partition property for normal ultrafilters on $P_κλ$, ibid., to appear.
• [4] K. Kunen, Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript, 1971.
• [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.
• [6] T. Menas, A combinatorial property of $P_κλ$, ibid. 41 (1976), 225-234.
• [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.
• [8] R. Solovay, W. Reinhardt, and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116.