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2000 | 166 | 1-2 | 137-151
Tytuł artykułu

On a problem of Steve Kalikow

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Kalikow problem for a pair (λ,κ) of cardinal numbers,λ > κ (in particular κ = 2) is whether we can map the family of ω-sequences from λ to the family of ω-sequences from κ in a very continuous manner. Namely, we demand that for η,ν ∈ ω we have: η, ν are almost equal if and only if their images are. We show consistency of the negative answer, e.g., for $ℵ_ω$ but we prove it for smaller cardinals. We indicate a close connection with the free subset property and its variants.
Słowa kluczowe
Rocznik
Tom
166
Numer
1-2
Strony
137-151
Opis fizyczny
Daty
wydano
2000
otrzymano
1996-09-02
poprawiono
1999-08-09
Twórcy
  • Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel, shelah@math.huji.ac.il
  • Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, U.S.A.
Bibliografia
  • [Ka90] S. Kalikow, Sequences of reals to sequences of zeros and ones, Proc. Amer. Math. Soc. 108 (1990), 833-837.
  • [Ko84] P. Koepke, The consistency strength of the free-subset property for $ω_ω$, J. Symbolic Logic 49 (1984), 1198-1204.
  • [Mi91] A. W. Miller, Arnie Miller's problem list, in: H. Judah (ed.), Set Theory of the Reals (Ramat Gan, 1991), Israel Math. Conf. Proc. 6, Bar-Ilan Univ., Ramat Gan, 1993, 645-654.
  • [Sh 76] S. Shelah, Independence of strong partition relation for small cardinals, and the free-subset problem, J. Symbolic Logic 45 (1980), 505-509.
  • [Sh 124] S. Shelah, $ℵ_ω$ may have a strong partition relation, Israel J. Math. 38 (1981), 283-288.
  • [Sh 110] S. Shelah, Better quasi-orders for uncountable cardinals, ibid. 42 (1982), 177-226.
  • [Sh:b] S. Shelah, Proper Forcing, Lecture Notes in Math. 940, Springer, Berlin, 1982.
  • [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994.
  • [Sh 481] S. Shelah, Was Sierpiński right? III Can continuum-c.c. times c.c.c. be continuum-c.c.? Ann. Pure Appl. Logic 78 (1996), 259-269.
  • [Sh:F254] S. Shelah, More on Kalikow Property of pairs of cardinals.
  • [Sh 513] S. Shelah, PCF and infinite free subsets, Arch. Math. Logic, to appear.
  • [Si70] J. Silver, A large cardinal in the constructible universe, Fund. Math. 69 (1970), 93-100.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv166i1p137bwm
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