4 found
  1.  3
    Infinitary Generalizations of Deligne’s Completeness Theorem.Christian Espíndola - forthcoming - Journal of Symbolic Logic:1-16.
  2.  25
    A Short Proof of Glivenko Theorems for Intermediate Predicate Logics.Christian Espíndola - 2013 - Archive for Mathematical Logic 52 (7-8):823-826.
    We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisting of instances of the principle of excluded middle for sentences (REM). We prove that both schemata combined derive classical logic, while each one of (...)
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  3.  18
    Infinitary First-Order Categorical Logic.Christian Espíndola - 2019 - Annals of Pure and Applied Logic 170 (2):137-162.
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    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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