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  1.  12
    Kripke Submodels and Universal Sentences.Ben Ellison, Jonathan Fleischmann, Dan McGinn & Wim Ruitenburg - 2007 - Mathematical Logic Quarterly 53 (3):311-320.
    We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in (...)
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  2.  30
    Syntactic Preservation Theorems for Intuitionistic Predicate Logic.Jonathan Fleischmann - 2010 - Notre Dame Journal of Formal Logic 51 (2):225-245.
    We define notions of homomorphism, submodel, and sandwich of Kripke models, and we define two syntactic operators analogous to universal and existential closure. Then we prove an intuitionistic analogue of the generalized (dual of the) Lyndon-Łoś-Tarski Theorem, which characterizes the sentences preserved under inverse images of homomorphisms of Kripke models, an intuitionistic analogue of the generalized Łoś-Tarski Theorem, which characterizes the sentences preserved under submodels of Kripke models, and an intuitionistic analogue of the generalized Keisler Sandwich Theorem, which characterizes the (...)
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  3.  22
    Quantifier Elimination for a Class of Intuitionistic Theories.Ben Ellison, Jonathan Fleischmann, Dan McGinn & Wim Ruitenburg - 2008 - Notre Dame Journal of Formal Logic 49 (3):281-293.
    From classical, Fraïissé-homogeneous, ($\leq \omega$)-categorical theories over finite relational languages, we construct intuitionistic theories that are complete, prove negations of classical tautologies, and admit quantifier elimination. We also determine the intuitionistic universal fragments of these theories.
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