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  1. Semantic Completeness of First-Order Theories in Constructive Reverse Mathematics.Christian Espíndola - 2016 - Notre Dame Journal of Formal Logic 57 (2):281-286.
    We introduce a general notion of semantic structure for first-order theories, covering a variety of constructions such as Tarski and Kripke semantics, and prove that, over Zermelo–Fraenkel set theory, the completeness of such semantics is equivalent to the Boolean prime ideal theorem. Using a result of McCarty, we conclude that the completeness of Kripke semantics is equivalent, over intuitionistic Zermelo–Fraenkel set theory, to the Law of Excluded Middle plus BPI. Along the way, we also prove the equivalence, over ZF, between (...)
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  • Some new intuitionistic equivalents of Zorn’s Lemma.John L. Bell - 2003 - Archive for Mathematical Logic 42 (8):811-814.
    Two new intuitionistic equivalents to Zarn’s Lemma are stated and proved.
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