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  1. Remarks on applicative theories.Andrea Cantini - 2005 - Annals of Pure and Applied Logic 136 (1-2):91-115.
    We deal with applicative theories which are based on combinatory logic with total application, extensionality and natural numbers. We prove a conservative extension theorem and two consistency results, involving principles of uniformity, reflection, enumeration and choice.
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  • Elementary explicit types and polynomial time operations.Daria Spescha & Thomas Strahm - 2009 - Mathematical Logic Quarterly 55 (3):245-258.
    This paper studies systems of explicit mathematics as introduced by Feferman [9, 11]. In particular, we propose weak explicit type systems with a restricted form of elementary comprehension whose provably terminating operations coincide with the functions on binary words that are computable in polynomial time. The systems considered are natural extensions of the first-order applicative theories introduced in Strahm [19, 20].
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