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Categorical characterizations of the natural numbers require primitive recursion
Annals of Pure and Applied Logic 166 (2):219-231 (2015)
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Citations of this work
Unifying the model theory of first-order and second-order arithmetic via WKL 0 ⁎.Ali Enayat & Tin Lok Wong - 2017 - Annals of Pure and Applied Logic 168 (6):1247-1283.
Weaker cousins of Ramsey's theorem over a weak base theory.Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk & Katarzyna W. Kowalik - 2021 - Annals of Pure and Applied Logic 172 (10):103028.
How Strong is Ramsey’s Theorem If Infinity Can Be Weak?Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik & Keita Yokoyama - 2023 - Journal of Symbolic Logic 88 (2):620-639.
Reverse mathematics, young diagrams, and the ascending chain condition.Kostas Hatzikiriakou & Stephen G. Simpson - 2017 - Journal of Symbolic Logic 82 (2):576-589.
Primitive recursive reverse mathematics.Nikolay Bazhenov, Marta Fiori-Carones, Lu Liu & Alexander Melnikov - 2024 - Annals of Pure and Applied Logic 175 (1):103354.
References found in this work
Cuts, consistency statements and interpretations.Pavel Pudlák - 1985 - Journal of Symbolic Logic 50 (2):423-441.
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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