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Shih-Ping Tung (1988). Definability on Formulas With Single Quantifier.

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    Arithmetic Definability by Formulas with Two Quantifiers.Shih Ping Tung - 1992 - Journal of Symbolic Logic 57 (1):1-11.
    We give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson.
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