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Eric Hall [6]Eric J. Hall [5]
  1.  91 DLs
    Eric J. Hall (2002). A Characterization of Permutation Models in Terms of Forcing. Notre Dame Journal of Formal Logic 43 (3):157-168.
    We show that if N and M are transitive models of ZFA such that N M, N and M have the same kernel and same set of atoms, and M AC, then N is a Fraenkel-Mostowski-Specker (FMS) submodel of M if and only if M is a generic extension of N by some almost homogeneous notion of forcing. We also develop a slightly modified notion of FMS submodels to characterize the case where M is a generic extension of N not (...)
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  2.  11 DLs
    Omar De la Cruz, Eric Hall, Paul Howard, Jean E. Rubin & Adrienne Stanley (2002). Definitions of Compactness and the Axiom of Choice. Journal of Symbolic Logic 67 (1):143-161.
    We study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.
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  3.  9 DLs
    Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Eleftherios Tachtsis (2005). Properties of the Real Line and Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 51 (6):598-609.
    We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals.
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  4.  6 DLs
    Omar De la Cruz, Eric J. Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2008). Unions and the Axiom of Choice. Mathematical Logic Quarterly 54 (6):652-665.
    We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union (...)
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  5.  4 DLs
    Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2003). Products of Compact Spaces and the Axiom of Choice II. Mathematical Logic Quarterly 49 (1):57-71.
    This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.
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  6.  3 DLs
    Eric J. Hall (2007). Permutation Models and SVC. Notre Dame Journal of Formal Logic 48 (2):229-235.
    Let M be a model of ZFAC (ZFC modified to allow a set of atoms), and let N be an inner model with the same set of atoms and the same pure sets (sets with no atoms in their transitive closure) as M. We show that N is a permutation submodel of M if and only if N satisfies the principle SVC (Small Violations of Choice), a weak form of the axiom of choice which says that in some sense, all (...)
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  7.  2 DLs
    Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin (2003). Metric Spaces and the Axiom of Choice. Mathematical Logic Quarterly 49 (5):455-466.
    We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.
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  8.  1 DLs
    P. Hinman & Eric J. Hall (2007). REVIEWS-Fundamentals of Mathematical Logic. Bulletin of Symbolic Logic 13 (3).
  9.  0 DLs
    Eric J. Hall, Kyriakos Keremedis & Eleftherios Tachtsis (2013). The Existence of Free Ultrafilters on Ω Does Not Imply the Extension of Filters on Ω to Ultrafilters. Mathematical Logic Quarterly 59 (4-5):258-267.
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