A note on a question of Abe
Burke, Douglas
Fundamenta Mathematicae, Tome 163 (2000), p. 95-98 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212432
@article{bwmeta1.element.bwnjournal-article-fmv163i1p95bwm,
     author = {Douglas Burke},
     title = {A note on a question of Abe},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {95-98},
     zbl = {0945.03068},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p95bwm}
}
Burke, Douglas. A note on a question of Abe. Fundamenta Mathematicae, Tome 163 (2000) pp. 95-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p95bwm/

[00000] [A] Y. Abe, Weakly normal ideals on Pκλ and the singular cardinal hypothesis, Fund. Math. 143 (1993), 97-106. | Zbl 0922.03063

[00001] [J] T. J. Jech, Set Theory, Academic Press, 1978.

[00002] [M1] M. Magidor, Precipitous ideals and Σ41 sets, Israel J. Math. 35 (1980), 109-134. | Zbl 0445.03023

[00003] [M2] D. A. Martin, Borel and Projective Games, book to be published.

[00004] [M3] Y. Matsubara, private communication.

[00005] [M4] Y. Matsubara, Saturated ideals and the singular cardinal hypothesis, J. Symbolic Logic 57 (1992), 970-974. | Zbl 0785.03037

[00006] [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.

[00007] [W1] W. H. Woodin, Supercompact cardinals and Σ12 sets, handwritten notes, May 1985.

[00008] [W2] W. H. Woodin, Supercompact cardinals, sets of reals, and weakly homogeneous trees, Proc. Nat. Acad. Sci. U.S.A. 85 (1988), 6587-6591. | Zbl 0656.03037