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  1. Jonathan P. Seldin (2011). Curry's Formalism as Structuralism. Logica Universalis 5 (1):91-100.
    In 1939, Curry proposed a philosophy of mathematics he called formalism. He made this proposal in two works originally written then, although one of them was not published until 1951. These are the two philosophical works for which Curry is known, and they have left a false impression of his views. In this article, I propose to clarify Curry’s views by referring to some of his later writings on the subject. I claim that Curry’s philosophy was not what is now (...)
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  2. Jonathan P. Seldin (2009). The Logic of Church and Curry. In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. 5--819.
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  3. Jonathan P. Seldin (2000). On the Role of Implication in Formal Logic. Journal of Symbolic Logic 65 (3):1076-1114.
    Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a "classical" version of the system. They can (...)
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  4. Jonathan P. Seldin (1999). Review: Jean-Pierre Ginisti, La Logique Combinatoire. [REVIEW] Journal of Symbolic Logic 64 (4):1833-1834.
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  5. Jonathan P. Seldin (1997). On the Proof Theory of Coquand's Calculus of Constructions. Annals of Pure and Applied Logic 83 (1):23-101.
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  6. Martin W. Bunder, J. Roger Hindley & Jonathan P. Seldin (1989). On Adding (Ξ) to Weak Equality in Combinatory Logic. Journal of Symbolic Logic 54 (2):590-607.
    Because the main difference between combinatory weak equality and λβ-equality is that the rule \begin{equation*}\tag{\xi} X = Y \vdash \lambda x.X = \lambda x.Y\end{equation*} is valid for the latter but not the former, it is easy to assume that another way of defining combinatory β-equality is to add rule (ξ) to the postulates for weak equality. However, to make this true, one must choose the definition of combinatory abstraction in (ξ) very carefully. If one tries to use one of the (...)
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  7. Jonathan P. Seldin (1989). Normalization and Excluded Middle. I. Studia Logica 48 (2):193 - 217.
    The usual rule used to obtain natural deduction formulations of classical logic from intuitionistic logic, namely.
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  8. Jonathan P. Seldin (1986). On the Proof Theory of the Intermediate Logic MH. Journal of Symbolic Logic 51 (3):626-647.
    A natural deduction formulation is given for the intermediate logic called MH by Gabbay in [4]. Proof-theoretic methods are used to show that every deduction can be normalized, that MH is the weakest intermediate logic for which the Glivenko theorem holds, and that the Craig-Lyndon interpolation theorem holds for it.
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  9. Jonathan P. Seldin (1980). A Second Corrigendum to My Paper: ``Note on Definitional Reductions''. Notre Dame Journal of Formal Logic 21 (4):728-728.
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  10. Jonathan P. Seldin (1979). Progress Report on Generalized Functionality. Annals of Mathematical Logic 17 (1-2):29-59.
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  11. M. W. Bunder & Jonathan P. Seldin (1978). Some Anomalies in Fitch's System QD. Journal of Symbolic Logic 43 (2):247-249.
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  12. Jonathan P. Seldin (1978). A Sequent Calculus Formulation of Type Assignment with Equality Rules for the \Ambdaβ-Calculus. Journal of Symbolic Logic 43 (4):643-649.
  13. Jonathan P. Seldin (1977). The ${\Bf Q}$-Consistency of ${\Cal F}_{22}$. Notre Dame Journal of Formal Logic 18 (1):117-127.
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  14. Jonathan P. Seldin (1977). A Sequent Calculus for Type Assignment. Journal of Symbolic Logic 42 (1):11-28.
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  15. Jonathan P. Seldin (1975). Arithmetic as a Study of Formal Systems. Notre Dame Journal of Formal Logic 16 (4):449-464.
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  16. Jonathan P. Seldin (1975). Review: Corrado Bohm, Wolf Gross, E. R. Caianiello, Introduction to the CUCH; C. Bohm, T. B. Steel, The CUCH as a Formal and Description Language. [REVIEW] Journal of Symbolic Logic 40 (1):81-83.
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  17. Jonathan P. Seldin (1975). Review: N. G. De Bruijn, Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem. [REVIEW] Journal of Symbolic Logic 40 (3):470-470.
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  18. Jonathan P. Seldin (1973). Equality in F21. Journal of Symbolic Logic 38 (4):571 - 575.
  19. Jonathan P. Seldin (1973). Equality in $Mathscr{F}_{21}$. Journal of Symbolic Logic 38 (4):571-575.
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  20. Jonathan P. Seldin (1973). Review: John T. Kearns, Combinatory Logic with Discriminators. [REVIEW] Journal of Symbolic Logic 38 (2):339-340.
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  21. Jonathan P. Seldin (1970). Review: Edward J. Cogan, A Formalization of the Theory of Sets From the Point of View of Combinatory Logic; Rainer Titgemeyer, Uber Einen Widerspruch in Cogans Darstellung der Mengenlehre. [REVIEW] Journal of Symbolic Logic 35 (1):147-147.
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  22. Jonathan P. Seldin (1970). Review: Maarten Wicher Visser Bunder, Set Theory Based on Combinatory Logic. [REVIEW] Journal of Symbolic Logic 35 (1):147-148.
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  23. Jonathan P. Seldin (1969). Corrigendum to My Paper: ``Note on Definitional Reductions''. Notre Dame Journal of Formal Logic 10 (4):412-412.
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  24. Jonathan P. Seldin (1968). Note on Definitional Reductions. Notre Dame Journal of Formal Logic 9 (1):4-6.
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