Some variations on the partition property for normal ultrafilters on Pkl

Julius Barbanel

Fundamenta Mathematicae (1993)

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

Abstract

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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 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.

How to cite

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Barbanel, 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

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  1. [1] J. B. Barbanel, Supercompact cardinals and trees of normal ultrafilters, J. Symbolic Logic 47 (1982), 89-109. Zbl0503.03025
  2. [2] J. B. Barbanel, Supercompact cardinals, trees of normal ultrafilters, and the partition property, ibid. 51 (1986), 701-708. Zbl0623.03051
  3. [3] 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. 
  4. [4] K. Kunen, Some remarks on theorems of Ketonen, Menas, and Solovay, unpublished handwritten manuscript, 1971. 
  5. [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. [6] T. Menas, A combinatorial property of P κ λ , ibid. 41 (1976), 225-234. 
  7. [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. [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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