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  1. Alberto Policriti & Eugenio Omodeo (2012). The Bernays—Schönfinkel—Ramsey Class for Set Theory: Decidability. Journal of Symbolic Logic 77 (3):896-918.
    As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.
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  2. Eugenio Omodeo & Alberto Policriti (2010). The Bernays-Schönfinkel-Ramsey Class for Set Theory: Semidecidability. Journal of Symbolic Logic 75 (2):459-480.
    As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...)
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  3. Andrea Formisano, Eugenio G. Omodeo & Ewa Orłowska (2006). An Environment for Specifying Properties of Dyadic Relations and Reasoning About Them II: Relational Presentation of Non-Classical Logics. In Harrie de Swart, Ewa Orlowska, Gunther Smith & Marc Roubens (eds.), Theory and Applications of Relational Structures as Knowledge Instruments Ii. Springer. 89--104.
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  4. Andrea Formisano, Eugenio G. Omodeo & Alberto Policriti (2005). The Axiom of Elementary Sets on the Edge of Peircean Expressibility. Journal of Symbolic Logic 70 (3):953 - 968.
    Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...)
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  5. Eugenio G. Omodeo, Franco Parlamento & Alberto Policriti (1996). Decidability of ∀*∀‐Sentences in Membership Theories. Mathematical Logic Quarterly 42 (1):41-58.
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  6. Eugenio Giovanni Omodeo (1980). Three Existence Principles in a Modal Calculus Without Descriptions Contained in A. Bressan's ${\Rm MC}^\Nu$. Notre Dame Journal of Formal Logic 21 (4):711-727.
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