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Eric Hall [7]Eric J. Hall [6]Eric E. Hall [2]
  1.  36
    Metric spaces and the axiom of choice.Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2003 - 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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  2.  49
    Products of compact spaces and the axiom of choice II.Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2003 - 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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  3.  10
    The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters.Eric J. Hall, Kyriakos Keremedis & Eleftherios Tachtsis - 2013 - Mathematical Logic Quarterly 59 (4-5):258-267.
    Let X be an infinite set and let and denote the propositions “every filter on X can be extended to an ultrafilter” and “X has a free ultrafilter”, respectively. We denote by the Stone space of the Boolean algebra of all subsets of X. We show: For every well‐ordered cardinal number ℵ, (ℵ) iff (2ℵ). iff “ is a continuous image of ” iff “ has a free open ultrafilter ” iff “every countably infinite subset of has a limit point”. (...)
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  4. A Characterization of Permutation Models in Terms of Forcing.Eric J. Hall - 2002 - 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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  5. Definitions of compactness and the axiom of choice.Omar De la Cruz, Eric Hall, Paul Howard, Jean E. Rubin & Adrienne Stanley - 2002 - 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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  6.  65
    Unions and the axiom of choice.Omar De la Cruz, Eric J. Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2008 - 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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  7.  49
    Properties of the real line and weak forms of the Axiom of Choice.Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Eleftherios Tachtsis - 2005 - 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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  8.  30
    Permutation Models and SVC.Eric J. Hall - 2007 - 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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  9.  3
    Independent families and some notions of finiteness.Eric Hall & Kyriakos Keremedis - 2023 - Archive for Mathematical Logic 62 (5):689-701.
    In \(\textbf{ZF}\), the well-known Fichtenholz–Kantorovich–Hausdorff theorem concerning the existence of independent families of _X_ of size \(|{\mathcal {P}} (X)|\) is equivalent to the following portion of the equally well-known Hewitt–Marczewski–Pondiczery theorem concerning the density of product spaces: “The product \({\textbf{2}}^{{\mathcal {P}}(X)}\) has a dense subset of size |_X_|”. However, the latter statement turns out to be strictly weaker than \(\textbf{AC}\) while the full Hewitt–Marczewski–Pondiczery theorem is equivalent to \(\textbf{AC}\). We study the relative strengths in \(\textbf{ZF}\) between the statement “_X_ has (...)
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  10.  1
    The Homebrewed Christianity guide to God: everything you ever wanted to know about the Almighty.Eric E. Hall - 2016 - Minneapolis: Fortress Presss. Edited by Tripp Fuller.
    In this latest installment of the Homebrewed Christianity series, Eric E. Hall approaches the question of God from various perspectives, including philosophy, personal revelation, Christian tradition, and other religions. At the end of this romp through history and pop culture, Hall argues that the God you need may be the very God you rejected years ago.--Back cover.
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  11.  3
    REVIEWS-Fundamentals of mathematical logic.P. Hinman & Eric J. Hall - 2007 - Bulletin of Symbolic Logic 13 (3):363-365.
  12.  6
    Groundless gods: the theological prospects of post-metaphysical thought.Hartmut von Sass & Eric E. Hall (eds.) - 2014 - Eugene, OR: Pickwick Publications.
    Groundless Gods: The Theological Prospects of Post-Metaphysical Thought deals with possible interpretations of an emerging interest in contemporary theology: postmetaphysical theology. This book attempts to openly come to grips, not only with what metaphysics and postmetaphysics imply, but also with what it could mean to do or not do theology from the standpoint of the nonmetaphysician. The book asks, for instance, whether this world has any singular definition, and whether God is some being standing apart from the world or an (...)
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