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  1. Arithmetical definability over finite structures.Troy Lee - 2003 - Mathematical Logic Quarterly 49 (4):385.
    Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform AC0 and FO. We prove finite analogs of three classic results in arithmetical definability, namely that < and TIMES can first-order define PLUS, that < and DIVIDES can first-order define TIMES, and that < and COPRIME can first-order define TIMES. The first result sharpens the equivalence FO =FO to FO = (...)
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  • Relatives of the Russell Paradox.Kees Doets - 1999 - Mathematical Logic Quarterly 45 (1):73-83.
    A formula ϕ in the one non-logical symbol ϵ with one free variable x is Russell if the sentence Vχ) is logically valid. This note describes a pattern common to the classical examples of Russell formulas, adds a couple of new ones, and constructs many formulas that are near-Russell.
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