Abstract
In this note we provide a straightforward translation \({{\mathcal{C}^{{\Gamma}}_{p}}}(T)\) for sets of formulas T and \(H_\Gamma(\exists x A(x))\) for existential formulas \(\exists x A(x)\) s.t. \({{\mathcal{C}^{{\Gamma}}_{p}}}(T) \vdash H_\Gamma(\exists x A(x))\) expresses “\(\exists x A(x)\) is derivable constructively from T iff it is derivable at all”.
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References
Baaz, M.: Note on a translation to characterize constructivity. J. Proc. Steklov Inst. Math. 242, 125–129 (2003)
Baaz, M.: Controlling witnesses. Annals of Pure and Applied Logic 136, 22–29 (2005)
Troelstra, A., van Dalen, D.: Constructivism in Mathematics, An Introduction, vol. 1. North-Holland, Amsterdam (1988)
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Baaz, M. (2007). Note on Conditional Constructivity. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds) Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science(), vol 4460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75939-3_2
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DOI: https://doi.org/10.1007/978-3-540-75939-3_2
Publisher Name: Springer, Berlin, Heidelberg
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