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  1. Many-Times Huge and Superhuge Cardinals.Julius B. Barbanel, Carlos A. Diprisco & It Beng Tan - 1984 - Journal of Symbolic Logic 49 (1):112-122.
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  2. Supercompact Cardinals, Trees of Normal Ultrafilters, and the Partition Property.Julius B. Barbanel - 1986 - Journal of Symbolic Logic 51 (3):701-708.
    Suppose κ is a supercompact cardinal. It is known that for every λ ≥ κ, many normal ultrafilters on P κ (λ) have the partition property. It is also known that certain large cardinal assumptions imply the existence of normal ultrafilters without the partition property. In [1], we introduced the tree T of normal ultrafilters associated with κ. We investigate the distribution throughout T of normal ultrafilters with and normal ultrafilters without the partition property.
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  3.  18
    Combinatorial Characterization of Supercompact Cardinals.Flipping Properties and Supercompact Cardinals.P Κ Λ-Generalizations of Weak Compactness.The Structure of Ineffability Properties of P Κ Λ.P Κ Λ Partition Relations.A Note on the Λ-Shelah Property. [REVIEW]Julius B. Barbanel - 1991 - Journal of Symbolic Logic 56 (3):1097.
  4. A Note on a Result of Kunen and Pelletier.Julius B. Barbanel - 1992 - Journal of Symbolic Logic 57 (2):461-465.
    Suppose that U and U' are normal ultrafilters associated with some supercompact cardinal. How may we compare U and U'? In what ways are they similar, and in what ways are they different? Partial answers are given in [1], [2], [3], [5], [6], and [7]. In this paper, we continue this study. In [6], Menas introduced a combinatorial principle χ(U) of normal ultrafilters U associated with supercompact cardinals, and showed that normal ultrafilters satisfying this property also satisfying this property also (...)
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  5.  31
    Two Applications of a Theorem of Dvoretsky, Wald, and Wolfovitz to Cake Division.Julius B. Barbanel & William S. Zwicker - 1997 - Theory and Decision 43 (2):203-207.
    In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we show that there exists a partition in which each player receives either more than, less than, or exactly his or her (...)
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  6.  10
    Supercompact Cardinals and Trees of Normal Ultrafilters.Julius B. Barbanel - 1982 - Journal of Symbolic Logic 47 (1):89-109.
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  7.  9
    [Omnibus Review].Julius B. Barbanel - 1991 - Journal of Symbolic Logic 56 (3):1097-1098.
    Reviewed Works:M. Magidor, Combinatorial Characterization of Supercompact Cardinals.Carlos A. Di Prisco, William S. Zwicker, Flipping Properties and Supercompact Cardinals.Donna M. Carr, $P_\kappa\lambda$-Generalizations of Weak Compactness.Donna M. Carr, The Structure of Ineffability Properties of $P_\kappa\lambda$.Donna M. Carr, $P_\kappa\lambda$ Partition Relations.Donna M. Carr, A Note on the $\lambda$-Shelah Property.
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  8.  8
    Supercompact Cardinals, Elementary Embeddings and Fixed Points.Julius B. Barbanel - 1982 - Journal of Symbolic Logic 47 (1):84-88.
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  9.  21
    On the Relationship Between the Partition Property and the Weak Partition Property for Normal Ultrafilters on $P_\Kappa\Lambda^1$.Julius B. Barbanel - 1993 - Journal of Symbolic Logic 58 (1):119-127.
    Suppose $\kappa$ is a supercompact cardinal and $\lambda > \kappa$. We study the relationship between the partition property and the weak partition property for normal ultrafilters on $P_\kappa\lambda$. On the one hand, we show that the following statement is consistent, given an appropriate large cardinal assumption: The partition property and the weak partition property are equivalent, there are many normal ultrafilters that satisfy these properties, and there are many normal ultrafilters that do not satisfy these properties. On the other hand, (...)
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