# A note on a question of Abe

Fundamenta Mathematicae (2000)

- Volume: 163, Issue: 1, page 95-98
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topBurke, Douglas. "A note on a question of Abe." Fundamenta Mathematicae 163.1 (2000): 95-98. <http://eudml.org/doc/212432>.

@article{Burke2000,

abstract = {Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V-ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.},

author = {Burke, Douglas},

journal = {Fundamenta Mathematicae},

keywords = {weakly normal filter; large cardinals; -complete filter; -ultrafilter; well-founded ultrapower},

language = {eng},

number = {1},

pages = {95-98},

title = {A note on a question of Abe},

url = {http://eudml.org/doc/212432},

volume = {163},

year = {2000},

}

TY - JOUR

AU - Burke, Douglas

TI - A note on a question of Abe

JO - Fundamenta Mathematicae

PY - 2000

VL - 163

IS - 1

SP - 95

EP - 98

AB - Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V-ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.

LA - eng

KW - weakly normal filter; large cardinals; -complete filter; -ultrafilter; well-founded ultrapower

UR - http://eudml.org/doc/212432

ER -

## References

top- [A] Y. Abe, Weakly normal ideals on ${P}_{\kappa}\lambda $ and the singular cardinal hypothesis, Fund. Math. 143 (1993), 97-106. Zbl0922.03063
- [J] T. J. Jech, Set Theory, Academic Press, 1978.
- [M1] M. Magidor, Precipitous ideals and ${\Sigma}_{4}^{1}$ sets, Israel J. Math. 35 (1980), 109-134. Zbl0445.03023
- [M2] D. A. Martin, Borel and Projective Games, book to be published.
- [M3] Y. Matsubara, private communication.
- [M4] Y. Matsubara, Saturated ideals and the singular cardinal hypothesis, J. Symbolic Logic 57 (1992), 970-974. Zbl0785.03037
- [S] R. M. Solovay, Strongly compact cardinals and the GCH, in: Proc. Tarski Symposium, Proc. Sympos. Pure Math. 25, Amer. Math. Soc., Providence, R.I., 1974, 365-372.
- [W1] W. H. Woodin, Supercompact cardinals and ${\Sigma}_{1}^{2}$ sets, handwritten notes, May 1985.
- [W2] W. H. Woodin, Supercompact cardinals, sets of reals, and weakly homogeneous trees, Proc. Nat. Acad. Sci. U.S.A. 85 (1988), 6587-6591. Zbl0656.03037

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.