16 citations · 67 across the 20 of their papers we have counts for
11 papers · 1 filter
A lower bound on Gowers' FIN_k theorem
Alexander P. Kreuzer
Gowers' FIN theorem, also called Gowers' pigeonhole principle or Gowers' theorem, is a Ramsey-type theorem. It first occurred in the study of Banach space theory and is a natur…
On the Uniform Computational Content of the Baire Category Theorem
Vasco Brattka, Matthew Hendtlass, Alexander P. Kreuzer
We study the uniform computational content of different versions of the Baire Category Theorem in the Weihrauch lattice. The Baire Category Theorem can be seen as a pigeonhole prin…
On the Uniform Computational Content of Computability Theory
Vasco Brattka, Matthew Hendtlass, Alexander P. Kreuzer
We demonstrate that the Weihrauch lattice can be used to classify the uniform computational content of computability-theoretic properties as well as the computational content of th…
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…
On idempotent ultrafilters in higher-order reverse mathematics
Alexander P. Kreuzer
We analyze the strength of the existence of idempotent ultrafilters in higher-order reverse mathematics. Let (Uidem) be the statement that an idempotent ultrafilter on the natural…
Non-principal ultrafilters, program extraction and higher order reverse mathematics
Alexander P. Kreuzer
We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let U be the statement that a non-principal ultrafilter exist…
On the strength of weak compactness
Alexander P. Kreuzer
We study the logical and computational strength of weak compactness in the separable Hilbert space \ell_2. Let weak-BW be the statement the every bounded sequence in \ell_2 has a w…
The cohesive principle and the Bolzano-Weierstraß principle
Alexander P. Kreuzer
The aim of this paper is to determine the logical and computational strength of instances of the Bolzano-Weierstraß principle (BW) and a weak variant of it. We show that BW is inst…