9 found
Sort by:
Disambiguations:
Eric Hall [6]Eric J. Hall [5]
  1. 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.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  2. 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  3. 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  4. P. Hinman & Eric J. Hall (2007). REVIEWS-Fundamentals of Mathematical Logic. Bulletin of Symbolic Logic 13 (3).
  5. 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.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  6. 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.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  7. 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.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  8. 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.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  9. 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 (...)
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation