16 citations · 67 across the 20 of their papers we have counts for
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Measure theory and higher order arithmetic
Alexander P. Kreuzer
We investigate the statement that the Lebesgue measure defined on all subsets of the Cantor space exists. As base system we take . The system $\mathsf{ACA}_0…
Bounded variation and the strength of Helly's selection theorem
Alexander P. Kreuzer
We analyze the strength of Helly's selection theorem HST, which is the most important compactness theorem on the space of functions of bounded variation. For this we utilize a new…
On principles between - and -induction, and monotone enumerations
Alexander P. Kreuzer, Keita Yokoyama
We show that many principles of first-order arithmetic, previously only known to lie strictly between -induction and -induction, are equivalent to the well-foundedness of…
Minimal idempotent ultrafilters and the Auslander-Ellis theorem
Alexander P. Kreuzer
We characterize the existence of minimal idempotent ultrafilters (on N) in the style of reverse mathematics and higher-order reverse mathematics using the Auslander-Ellis theorem a…