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The model companion of the theory of fields with valuation and automorphism (of the pure field structure) exists. A counterexample shows that the theory of models of ACFA equipped with valuation is not this model companion.
We use set-theoretic tools to make a model-theoretic contribution. In particular, we construct a...
Anderson and Csima (Notre Dame J Form Log 55:245–264, 2014) defined a bounded jump operator for bounded-Turing reduction, and studied its basic properties. Anderson et al. (Arch Math Logic 56:507–521, 2017) constructed a low bounded-high set and conjectured that such sets cannot be computably...
We investigate the classes of ideals for which the Egoroff’s theorem or the generalized Egoroff’s theorem holds between ideal versions of pointwise and uniform convergences. The paper is motivated by considerations of Korch (Real Anal Exchange 42(2):269–282, 2017).
In this note we study several topics related to the schema of local reflection...
The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We...
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