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  1.  7
    The First Omitting Cardinal for Magidority.Shimon Garti & Yair Hayut - 2019 - Mathematical Logic Quarterly 65 (1):95-104.
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  2.  18
    Depth of Boolean Algebras.Shimon Garti & Saharon Shelah - 2011 - Notre Dame Journal of Formal Logic 52 (3):307-314.
    Suppose $D$ is an ultrafilter on $\kappa$ and $\lambda^\kappa = \lambda$. We prove that if ${\bf B}_i$ is a Boolean algebra for every $i.
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  3.  9
    On the Spectrum of Characters of Ultrafilters.Shimon Garti, Menachem Magidor & Saharon Shelah - 2018 - Notre Dame Journal of Formal Logic 59 (3):371-379.
    We show that the character spectrum Spχ may include any prescribed set of regular cardinals between λ and 2λ.
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  4.  24
    A Strong Polarized Relation.Shimon Garti & Saharon Shelah - 2012 - Journal of Symbolic Logic 77 (3):766-776.
    We prove that the strong polarized relation $\left( {\mu _\mu ^ + } \right) \to \left( {\mu _\mu ^ + } \right)_2^{1.1}$ is consistent with ZFC, for a singular ì which is a limit of measurable cardinals.
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  5.  5
    Many Normal Measures.Shimon Garti - 2014 - Notre Dame Journal of Formal Logic 55 (3):349-357.
    We characterize the situation of having at least $^{+}$-many normal ultrafilters on a measurable cardinal $\kappa$. We also show that if $\kappa$ is a compact cardinal, then $\kappa$ carries $^{+}$-many $\kappa$-complete ultrafilters, each of which extends the club filter on $\kappa$.
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  6.  4
    Two Cardinal Models for Singular Μ.Shimon Garti & Saharon Shelah - 2007 - Mathematical Logic Quarterly 53 (6):636-641.
    We deal here with colorings of the pair , when μ is a strong limit and singular cardinal. We show that there exists a coloring c with no refinement. It follows that the properties of colorings of when μ is singular differ in an essential way from the case of regular μ.
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