A note on a question of Abe

Douglas Burke

Fundamenta Mathematicae (2000)

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

Abstract

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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.

How to cite

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Burke, 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

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  1. [A] Y. Abe, Weakly normal ideals on P κ λ and the singular cardinal hypothesis, Fund. Math. 143 (1993), 97-106. Zbl0922.03063
  2. [J] T. J. Jech, Set Theory, Academic Press, 1978. 
  3. [M1] M. Magidor, Precipitous ideals and Σ 4 1 sets, Israel J. Math. 35 (1980), 109-134. Zbl0445.03023
  4. [M2] D. A. Martin, Borel and Projective Games, book to be published. 
  5. [M3] Y. Matsubara, private communication. 
  6. [M4] Y. Matsubara, Saturated ideals and the singular cardinal hypothesis, J. Symbolic Logic 57 (1992), 970-974. Zbl0785.03037
  7. [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. 
  8. [W1] W. H. Woodin, Supercompact cardinals and Σ 1 2 sets, handwritten notes, May 1985. 
  9. [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

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