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Paul Howard [25]Paul E. Howard [9]
  1. Paul Howard & Eleftherios Tachtsis (2013). On Vector Spaces Over Specific Fields Without Choice. Mathematical Logic Quarterly 59 (3):128-146.
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  2. Paul Howard (2011). The Finiteness of Compact Boolean Algebras. Mathematical Logic Quarterly 57 (1):14-18.
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  3. 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.
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  4. Paul Howard (2007). Bases, Spanning Sets, and the Axiom of Choice. Mathematical Logic Quarterly 53 (3):247-254.
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  5. David Blair, Andreas Blass & Paul Howard (2005). Divisibility of Dedekind Finite Sets. Journal of Mathematical Logic 5 (01):49-85.
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  6. 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.
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  7. Paul Howard (2005). If Vector Spaces Are Projective Modules Then Multiple Choice Holds. Mathematical Logic Quarterly 51 (2):187.
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  8. 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.
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  9. 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.
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  10. O. De la Cruz, Paul Howard & E. Hall (2002). Products of Compact Spaces and the Axiom of Choice. Mathematical Logic Quarterly 48 (4):508-516.
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  11. 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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  12. J. E. Rubin, K. Keremedis & Paul Howard (2001). Non-Constructive Properties of the Real Numbers. Mathematical Logic Quarterly 47 (3):423-431.
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  13. Paul Howard, K. Keremedis & J. E. Rubin (2000). Compactness in Countable Tychonoff Products and Choice. Mathematical Logic Quarterly 46 (1):3-16.
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  14. Paul Howard, K. Keremedis & J. E. Rubin (2000). Paracompactness of Metric Spaces and the Axiom of Multiple Choice. Mathematical Logic Quarterly 46 (2):219-232.
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  15. Paul Howard, J. E. Rubin & A. Stanley (2000). Von Rimscha's Transitivity Conditions. Mathematical Logic Quarterly 46 (4):549-554.
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  16. Paul Howard, Kyriakos Keremedis, Herman Rubin & Jean E. Rubin (1998). Disjoint Unions of Topological Spaces and Choice. Mathematical Logic Quarterly 44 (4):493-508.
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  17. Paul Howard, Kyriakos Keremedis, Herman Rubin & Jean E. Rubin (1998). Versions of Normality and Some Weak Forms of the Axiom of Choice. Mathematical Logic Quarterly 44 (3):367-382.
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  18. Paul Howard & Jean E. Rubin (1996). The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice. Mathematical Logic Quarterly 42 (1):410-420.
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  19. Paul Howard & Jean E. Rubin (1995). The Axiom of Choice for Well-Ordered Families and for Families of Well- Orderable Sets. Journal of Symbolic Logic 60 (4):1115-1117.
    We show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets are both true, but the axiom of choice is false.
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  20. Hartmut Höft & Paul Howard (1994). Well Ordered Subsets of Linearly Ordered Sets. Notre Dame Journal of Formal Logic 35 (3):413-425.
    The deductive relationships between six statements are examined in set theory without the axiom of choice. Each of these statements follows from the axiom of choice and involves linear orderings in some way.
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  21. Paul Howard (1993). Variations of Rado's Lemma. Mathematical Logic Quarterly 39 (1):353-356.
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  22. Norbert Brunner & Paul Howard (1992). Russell's Alternative to the Axiom of Choice. Mathematical Logic Quarterly 38 (1):529-534.
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  23. Paul E. Howard (1992). The Axiom of Choice for Countable Collections of Countable Sets Does Not Imply the Countable Union Theorem. Notre Dame Journal of Formal Logic 33 (2):236-243.
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  24. Paul Howard & Jeffrey Solski (1992). The Strength of the $\Delta$-System Lemma. Notre Dame Journal of Formal Logic 34 (1):100-106.
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  25. Paul E. Howard (1990). Definitions of Compact. Journal of Symbolic Logic 55 (2):645-655.
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  26. Paul E. Howard (1987). The Existence of Level Sets in a Free Group Implies the Axiom of Choice. Mathematical Logic Quarterly 33 (4):315-316.
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  27. Paul E. Howard & Mary Yorke (1987). Maximal $P$-Subgroups and the Axiom of Choice. Notre Dame Journal of Formal Logic 28 (2):276-283.
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  28. Paul E. Howard (1985). Subgroups of a Free Group and the Axiom of Choice. Journal of Symbolic Logic 50 (2):458-467.
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  29. Paul E. Howard (1984). Rado's Selection Lemma Does Not Imply the Boolean Prime Ideal Theorem. Mathematical Logic Quarterly 30 (9‐11):129-132.
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  30. Paul E. Howard, Arthur L. Rubin & Jean E. Rubin (1978). Independence Results for Class Forms of the Axiom of Choice. Journal of Symbolic Logic 43 (4):673-684.
    Let NBG be von Neumann-Bernays-Gödel set theory without the axiom of choice and let NBGA be the modification which allows atoms. In this paper we consider some of the well-known class or global forms of the wellordering theorem, the axiom of choice, and maximal principles which are known to be equivalent in NBG and show they are not equivalent in NBGA.
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  31. Hartmut Höft & Paul Howard (1973). A Graph Theoretic Equivalent to the Axiom of Choice. Mathematical Logic Quarterly 19 (11‐12):191-191.
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  32. Paul E. Howard (1973). Limitations on the Fraenkel-Mostowski Method of Independence Proofs. Journal of Symbolic Logic 38 (3):416-422.
    The Fraenkel-Mostowski method has been widely used to prove independence results among weak versions of the axiom of choice. In this paper it is shown that certain statements cannot be proved by this method. More specifically it is shown that in all Fraenkel-Mostowski models the following hold: 1. The axiom of choice for sets of finite sets implies the axiom of choice for sets of well-orderable sets. 2. The Boolean prime ideal theorem implies a weakened form of Sikorski's theorem.
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  33. Paul E. Howard (1972). A Proof of a Theorem of Tennenbaum. Mathematical Logic Quarterly 18 (7):111-112.
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