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1993 | 143 | 2 | 97-106
Tytuł artykułu

Weakly normal ideals ou PKl and the singular cardinal hypothesis

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay's theorem concerning strongly compact cardinals, we show that $λ^{<κ}$ is decided if $P_κλ$ carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.
Słowa kluczowe
Rocznik
Tom
143
Numer
2
Strony
97-106
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-11-05
Twórcy
  • Numazu College of Technology, 3600 Ooka, Numazu-Shi, Shizuoka, 410 Japan
  • Department of Mathematics, Kanagawa University, Rokkakubashi, Kanagawa-Ku, Yokohama 221, Japan
Bibliografia
  • [1] Y. Abe, Weakly normal filters and the closed unbounded filter on $P_κ λ$, Proc. Amer. Math. Soc. 104 (1988), 1226-1234.
  • [2] Y. Abe, Saturated ideals and subtle properties of $P_κ λ$, circulated.
  • [3] Y. Abe, Weakly normal filters and large cardinals, Tsukuba J. Math. 16 (1992), 487-494.
  • [4] D. M. Carr, The minimal normal filter on $P_κ λ$, Proc. Amer. Math. Soc. 86 (1982), 316-320.
  • [5] M. Foreman, Potent axioms, Trans. Amer. Math. Soc. 294 (1986), 1-28.
  • [6] C. A. Johnson, On ideals and stationary reflection, J. Symbolic Logic 54 (1989), 568-575.
  • [7] A. Kanamori, Weakly normal filters and irregular ultrafilters, Trans. Amer. Math. Soc. 220 (1976), 393-399.
  • [8] Y. Matsubara, Menas's conjecture and generic ultrapowers, Ann. Pure Appl. Logic 36 (1987), 225-234.
  • [9] Y. Matsubara, private communication.
  • [10] R. Mignone, A direct weakening of normality for filters, preprint.
  • [11] M. Shioya, Weakly normal closures of filters on $P_κ λ$, to appear.
  • [12] J. Silver, On the singular cardinals problem, in: Proc. Internat. Congress Math. Vancouver, 1974, 265-268.
  • [13] R. M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory, Proc. Sympos. Pure Math. 13 I, D. Scott (ed.), Amer. Math. Soc., Providence, R.I., 1971, 397-428.
  • [14] 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.
  • [15] R. M. Solovay, W. N. Reinhardt and A. Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), 73-116.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv143i2p97bwm
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