A note on a question of Abe

• Autorzy: Douglas Burke
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E40: Other aspects of forcing and Boolean-valued models

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 1
• Strony: 95-98

Daty

wydano

2000

otrzymano

1999-09-01

Twórcy

autor

Douglas Burke

• Department of Mathematics, University of Nevada, Las Vegas, NV 89154, U.S.A.

Bibliografia

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• [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.
• [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 $Σ^2_1$ 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.