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math.LO2022
Kreisel-Lévy-type theorems for Kripke-Platek and other set theories
Shuangshuang Shu, Michael Rathjen
We prove that, over Kripke-Platek set theory with infinity (KP), transfinite induction along the ordinal is equivalent to the schema asserting the soundness of KP, where…
math.LO2022
Constructing the Constructible Universe Constructively
Richard Matthews, Michael Rathjen
We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the univer…
math.LO2022
Admissible extensions of subtheories of second order arithmetic
Gerhard Jäger, Michael Rathjen
In this paper we study admissible extensions of several theories T of reverse mathematics. The idea is that in such an extension the structure M = (N,S,\in) of the natural numbers…