Search Results - "Kreuzer, Alexander P."

On the Uniform Computational Content of Computability Theory by Brattka, Vasco, Hendtlass, Matthew, Kreuzer, Alexander P.

“…We demonstrate that the Weihrauch lattice can be used to classify the uniform computational content of computability-theoretic properties as well as the…”
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Measure theory and higher order arithmetic by KREUZER, ALEXANDER P.

“…We obtain that over \mathsf {ACA_0}^\omega + (\mu )-conservative over \mathsf {ACA_0}^\omega . Moreover, we establish a corresponding program extraction…”
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Bounded variation and the strength of Helly's selection theorem by Kreuzer, Alexander P.

“…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…”
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From Bolzano-Weierstraß to Arzelà-Ascoli by Kreuzer, Alexander P.

“…We show how one can obtain solutions to the Arzelà‐Ascoli theorem using suitable applications of the Bolzano‐Weierstraß principle. With this, we can apply the…”
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Program extraction for 2-random reals by Kreuzer, Alexander P.

“…Let be the statement that for each real X a real 2-random relative to X exists. We apply program extraction techniques we developed in Kreuzer and Kohlenbach…”
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The cohesive principle and the Bolzano-Weierstraß principle by Kreuzer, Alexander P.

“…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…”
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Term extraction and Ramsey's theorem for pairs by Kreuzer, Alexander P., Kohlenbach, Ulrich

“…In this paper we study with proof-theoretic methods the function(al) s provably recursive relative to Ramsey's theorem for pairs and the cohesive principle…”
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ON IDEMPOTENT ULTRAFILTERS IN HIGHER-ORDER REVERSE MATHEMATICS by KREUZER, ALEXANDER P.

“…We analyze the strength of the existence of idempotent ultrafilters in higher-order reverse mathematics. Let (uidem) be the statement that an idempotent…”
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A logical analysis of the generalized Banach contractions principle by Kreuzer, Alexander

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A lower bound on Gowers' FIN_k theorem by Kreuzer, Alexander P

“…Gowers' FIN$_k$ theorem, also called Gowers' pigeonhole principle or Gowers' theorem, is a Ramsey-type theorem. It first occurred in the study of Banach space…”
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Bounded variation and the strength of Helly's selection theorem by Kreuzer, Alexander P

“…Logical Methods in Computer Science, Volume 10, Issue 4 (December 24, 2014) lmcs:980 We analyze the strength of Helly's selection theorem HST, which is the…”
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On the Uniform Computational Content of Computability Theory by Brattka, Vasco, Hendtlass, Matthew, Kreuzer, Alexander P

“…Theory of Computing Systems 61:4 (2017) 1376-1426 We demonstrate that the Weihrauch lattice can be used to classify the uniform computational content of…”
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Measure theory and higher order arithmetic by Kreuzer, Alexander P

“…We investigate the statement that the Lebesgue measure defined on all subsets of the Cantor space exists. As base system we take $\mathsf{ACA}_0^\omega +…”
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Minimal idempotent ultrafilters and the Auslander-Ellis theorem by Kreuzer, Alexander P

“…We characterize the existence of minimal idempotent ultrafilters (on N) in the style of reverse mathematics and higher-order reverse mathematics using the…”
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On the Uniform Computational Content of the Baire Category Theorem by Brattka, Vasco, Hendtlass, Matthew, Kreuzer, Alexander P

“…Notre Dame J. Formal Logic 59, no. 4 (2018), 605-636 We study the uniform computational content of different versions of the Baire Category Theorem in the…”
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On idempotent ultrafilters in higher-order reverse mathematics by Kreuzer, Alexander P

“…J. of Symbolic Logic vol. 80 (2015), no. 1, pp. 179-193 We analyze the strength of the existence of idempotent ultrafilters in higher-order reverse…”
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WaLDORf: Wasteless Language-model Distillation On Reading-comprehension by Tian, James Yi, Kreuzer, Alexander P, Chen, Pai-Hung, Will, Hans-Martin

“…Transformer based Very Large Language Models (VLLMs) like BERT, XLNet and RoBERTa, have recently shown tremendous performance on a large variety of Natural…”
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From Bolzano-Weierstra{\ss} to Arzel\`a-Ascoli by Kreuzer, Alexander P

“…Mathematical Logic Quarterly, vol. 60 (2014), no. 3, pp. 177-183 We show how one can obtain solutions to the Arzel\`a-Ascoli theorem using suitable…”
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Non-principal ultrafilters, program extraction and higher order reverse mathematics by Kreuzer, Alexander P

“…J. of Mathmatical Logic, vol. 12 (2012), no 1 We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order…”
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On principles between $\Sigma_1$- and $\Sigma_2$-induction, and monotone enumerations by Kreuzer, Alexander P, Yokoyama, Keita

“…We show that many principles of first-order arithmetic, previously only known to lie strictly between $\Sigma_1$-induction and $\Sigma_2$-induction, are…”
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