11 found
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  1. Stability of Nilpotent Groups of Class 2 and Prime Exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.
    Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.
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  2. C. C. C. Forcing Without Combinatorics.Alan H. Mekler - 1984 - Journal of Symbolic Logic 49 (3):830-832.
    c.c.c. posets are characterised in terms of N-generic conditions. This characterisation can be applied to get simple proofs of many facts about c.c.c. forcing including $\operatorname{Con}(MA + \neg CH)$.
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  3. Uniformization Principles.Alan H. Mekler & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (2):441-459.
    It is consistent that for many cardinals λ there is a family of at least λ + unbounded subsets of λ which have uniformization properties. In particular if it is consistent that a supercompact cardinal exists, then it is consistent that ℵ ω has such a family. We have applications to point set topology, Whitehead groups and reconstructing separable abelian p-groups from their socles.
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  4.  9
    Stationary Logic and its Friends. I.Alan H. Mekler & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):129-138.
  5.  23
    Universal Structures in Power ℵ1.Alan H. Mekler - 1990 - Journal of Symbolic Logic 55 (2):466-477.
    It is consistent with ¬CH that every universal theory of relational structures with the joint embedding property and amalgamation for P --diagrams has a universal model of cardinality ℵ 1. For classes with amalgamation for P --diagrams it is consistent that $2^{\aleph_0} > \aleph_2$ and there is a universal model of cardinality ℵ 2.
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  6.  8
    Stationary Logic and its Friends. II.Alan H. Mekler & Saharon Shelah - 1986 - Notre Dame Journal of Formal Logic 27 (1):39-50.
  7.  6
    Categoricity Results for L∞Κ.Paul C. Eklof & Alan H. Mekler - 1988 - Annals of Pure and Applied Logic 37 (1):81-99.
  8.  13
    Stationary Logic of Ordinals.Alan H. Mekler - 1984 - Annals of Pure and Applied Logic 26 (1):47-68.
  9.  22
    On the Logic of Continuous Algebras.Jiří Adámek, Alan H. Mekler, Evelyn Nelson & Jan Reiterman - 1988 - Notre Dame Journal of Formal Logic 29 (3):365-380.
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  10.  6
    Universal Structures in Power $Aleph_1$.Alan H. Mekler - 1990 - Journal of Symbolic Logic 55 (2):466-477.
    It is consistent with $\neg\mathrm{CH}$ that every universal theory of relational structures with the joint embedding property and amalgamation for $\mathscr{P}^-(3)$-diagrams has a universal model of cardinality $\aleph_1$. For classes with amalgamation for $\mathscr{P}^-(4)$-diagrams it is consistent that $2^{\aleph_0} > \aleph_2$ and there is a universal model of cardinality $\aleph_2$.
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  11.  1
    Categoricity Results for< I> L_< Sub>∞ Κ.Paul C. Eklof & Alan H. Mekler - 1988 - Annals of Pure and Applied Logic 37 (1):81-99.