Categorical characterizations of the natural numbers require primitive recursion

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Annals of Pure and Applied Logic 166 (2):219-231 (2015)
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10.1016/j.apal.2014.10.003

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Cuts, consistency statements and interpretations.Pavel Pudlák - 1985 - Journal of Symbolic Logic 50 (2):423-441.
Second order logic or set theory?Jouko Väänänen - 2012 - Bulletin of Symbolic Logic 18 (1):91-121.
Reverse mathematics and Peano categoricity.Stephen G. Simpson & Keita Yokoyama - 2013 - Annals of Pure and Applied Logic 164 (3):284-293.
The self-embedding theorem of WKL0 and a non-standard method.Kazuyuki Tanaka - 1997 - Annals of Pure and Applied Logic 84 (1):41-49.
Second-order and higher-order logic.Herbert B. Enderton - 2008 - Stanford Encyclopedia of Philosophy.

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