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math.LO2014
End-extensions of models of weak arithmetic from complexity-theoretic containments
Leszek Aleksander Kołodziejczyk
We prove that if the linear-time and polynomial-time hierarchies coincide, then every model of has a proper end-extension to a model of $Π_1(\mathbb{N}…
math.LO2014
Categorical characterizations of the natural numbers require primitive recursion
Leszek Aleksander Kołodziejczyk, Keita Yokoyama
Simpson and the second author asked whether there exists a characterization of the natural numbers by a second-order sentence which is provably categorical in the theory RCA.…