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  1. 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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  2. Paul E. Howard (1990). Definitions of Compact. Journal of Symbolic Logic 55 (2):645-655.
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  3. 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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  4. 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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  5. 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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  6. 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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  7. 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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  8. 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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  9. Paul E. Howard (1972). A Proof of a Theorem of Tennenbaum. Mathematical Logic Quarterly 18 (7):111-112.
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