# Some variations on the partition property for normal ultrafilters on Pkl

Fundamenta Mathematicae (1993)

- Volume: 142, Issue: 2, page 163-171
- ISSN: 0016-2736

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topBarbanel, Julius. "Some variations on the partition property for normal ultrafilters on Pkl." Fundamenta Mathematicae 142.2 (1993): 163-171. <http://eudml.org/doc/211979>.

@article{Barbanel1993,

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 $P_κλ$. 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.},

author = {Barbanel, Julius},

journal = {Fundamenta Mathematicae},

keywords = {supercompact cardinal; weak partition property},

language = {eng},

number = {2},

pages = {163-171},

title = {Some variations on the partition property for normal ultrafilters on Pkl},

url = {http://eudml.org/doc/211979},

volume = {142},

year = {1993},

}

TY - JOUR

AU - Barbanel, Julius

TI - Some variations on the partition property for normal ultrafilters on Pkl

JO - Fundamenta Mathematicae

PY - 1993

VL - 142

IS - 2

SP - 163

EP - 171

AB - 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.

LA - eng

KW - supercompact cardinal; weak partition property

UR - http://eudml.org/doc/211979

ER -

## References

top- [1] J. B. Barbanel, Supercompact cardinals and trees of normal ultrafilters, J. Symbolic Logic 47 (1982), 89-109. Zbl0503.03025
- [2] J. B. Barbanel, Supercompact cardinals, trees of normal ultrafilters, and the partition property, ibid. 51 (1986), 701-708. Zbl0623.03051
- [3] J. B. Barbanel, On the relationship between the partition property and the weak partition property for normal ultrafilters on ${P}_{\kappa}\lambda $, 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- [4] K. Kunen, Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript, 1971.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. Zbl0548.03031
- [6] T. Menas, A combinatorial property of ${P}_{\kappa}\lambda $, 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. Zbl0317.02083
- [8] R. Solovay, W. Reinhardt, and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116. Zbl0376.02055

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