13 found
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  1.  21
    Maxim R. Burke and Menachem Magidor. Shelah's Pcf Theory and its Applications. Annals of Pure and Applied Logic, Vol. 50 , Pp. 207–254. [REVIEW]Menachem Kojman - 2002 - Bulletin of Symbolic Logic 8 (2):307-308.
  2.  21
    Continuous Ramsey Theory on Polish Spaces and Covering the Plane by Functions.Stefan Geschke, Martin Goldstern & Menachem Kojman - 2004 - Journal of Mathematical Logic 4 (2):109-145.
  3.  14
    Thomas Jech. Singular Cardinal Problem: Shelah's Theorem on 2ℵω. Bulletin of the London Mathematical Society, Vol. 24 , Pp. 127–139. [REVIEW]Menachem Kojman - 2002 - Bulletin of Symbolic Logic 8 (2):308.
  4. Nonexistence of Universal Orders in Many Cardinals.Menachem Kojman & Saharon Shelah - 1992 - Journal of Symbolic Logic 57 (3):875-891.
    Our theme is that not every interesting question in set theory is independent of ZFC. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZFC a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove--again in ZFC--that for a large class of cardinals there is no universal linear order (e.g. in every regular $\aleph_1 < (...)
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  5.  8
    The Universality Spectrum of Stable Unsuperstable Theories.Menachem Kojman & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (1):57-72.
    Kojman, M. and S. Shelah, The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic 58 57–72. It is shown that if T is stable unsuperstable, and 1 [brvbar]T[brvbar], T stable and κ<κ then there is a universal tree of height κ + 1 in cardinality λ.
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  6.  16
    Μ-Complete Souslin Trees on Μ+.Menachem Kojman & Saharon Shelah - 1993 - Archive for Mathematical Logic 32 (3):195-201.
    We prove thatµ=µ <µ , 2 µ =µ + and “there is a non-reflecting stationary subset ofµ + composed of ordinals of cofinality <μ” imply that there is a μ-complete Souslin tree onµ +.
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  7.  7
    The PCF Trichotomy Theorem Does Not Hold for Short Sequences.Menachem Kojman & Saharon Shelah - 2000 - Archive for Mathematical Logic 39 (3):213-218.
    . The PCF Trichotomy Theorem deals with sequences of ordinal functions on an infinite $\kappa$ modulo some ideal I. If a $<_I$ -increasing sequence of ordinal functions has regular length which is larger than $\kappa^+$ , then by the Trichotomy Theorem the sequence satisfies one of three structural conditions. It was of some interest to find out if the Trichotomy Theorem could hold also for sequences of length $\kappa^+$ . It is shown that this is not the case.
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  8.  5
    Exact Upper Bounds and Their Uses in Set Theory.Menachem Kojman - 1998 - Annals of Pure and Applied Logic 92 (3):267-282.
    The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem gives a necessary and sufficient condition for the existence of an exact upper bound ƒ for a ¦A¦+ is regular: an eub ƒ with lim infI cf ƒ = μ exists if and only if for every regular κ ε the set of flat points in tf of cofinality κ is stationary. Two applications of the main Theorem to set theory (...)
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  9.  4
    Preface.Menachem Kojman - 2006 - Annals of Pure and Applied Logic 140 (1-3):1-2.
  10.  3
    Fallen Cardinals.Menachem Kojman & Saharon Shelah - 2001 - Annals of Pure and Applied Logic 109 (1-2):117-129.
    We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra contains a complete subalgebra which is isomorphic to the collapse algebra CompCol. Consequently, adding a generic filter to the quotient algebra collapses μ0 to 1. Another corollary is that the Baire number of the space U of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory.
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  11.  12
    A Proof of Shelah's Partition Theorem.Menachem Kojman - 1995 - Archive for Mathematical Logic 34 (4):263-268.
    A self contained proof of Shelah's theorem is presented: If μ is a strong limit singular cardinal of uncountable cofinality and 2μ > μ+ then $\left( {\begin{array}{*{20}c} {\mu ^ + } \\ \mu \\ \end{array} } \right) \to \left( {\begin{array}{*{20}c} {\mu ^ + } \\ {\mu + 1} \\ \end{array} } \right)_{< cf\mu } $.
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  12. 2003 European Summer Meeting of the Association for Symbolic Logic Logic Colloquim'03.Michael Benedikt, Stevo Todorcevic, Alexandru Baltag, Howard Becker, Matthew Foreman, Jean-Yves Girard, Martin Grohe, Peter T. Johnstone, Simo Knuuttila & Menachem Kojman - 2004 - Bulletin of Symbolic Logic 10 (2).
  13.  14
    Review: Maxim R. Burke, Menachem Magidor, Shelah's Pcf Theory and Its Applications. [REVIEW]Menachem Kojman - 2002 - Bulletin of Symbolic Logic 8 (2):307-308.