Alexander Kreuzer's homepage

I moved to ENS Lyon.
My new Homagepage is located at
http://perso.ens-lyon.fr/alexander.kreuzer/.

I am a postdoc in the workgroup of Prof. Kohlenbach at the mathematics department of TU Darmstadt.

Address:
Technische Universität Darmstadt
Fachbereich Mathematik, AG Logik
Schloßgartenstraße 7
64289 Darmstadt
Germany

Office: S215/203

Phone: +49 (6151) 16-2860

Email: akreuzer [at] mathematik [dot] tu-darmstadt [dot] de

Papers:

1. Ramsey's Theorem for pairs and provably recursive functions (with Ulrich Kohlenbach).
   Final version in: Notre Dame Journal of Formal Logic, vol. 50 (2009), no. 4, pp. 427-444.
   [doi:10.1215/00294527-2009-019] [MR 2598872]
2. The cohesive principle and the Bolzano-Weierstraß principle.
   Preprint at arXiv:1005.5316.
   Final version in: Mathematical Logic Quarterly, vol. 57 (2011), no. 3, pp. 292-298.
   [doi:10.1002/malq.2010100089] [MR 2839129]
3. Term extraction and Ramsey's theorem for pairs (with Ulrich Kohlenbach).
   Final version in: J. Symbolic Logic vol. 77 (2012), no. 3, pp. 853-895. [LINK]
4. Primitive recursion and the chain antichain principle.
   Final version in: Notre Dame J. Formal Logic, vol. 53 (2012), no. 2, 245-265.
   [doi:10.1215/00294527-1715716]
5. On the strength of weak compactness. Preprint available at arXiv:1106.5124. Updated preprint.
   Final version to appear in Computability - Journal of the CiE.
6. Non-principal ultrafilters, program extraction and higher order reverse mathematics. Preprint available at arXiv:1109.4277.
   Updated preprint.
   Final version in: J. of Mathmatical Logic, vol. 12 (2012), no 1.
   [doi:10.1142/S021906131250002X]
7. From Bolzano-Weierstraß to Arzelà-Ascoli.
   Submitted. arXiv:1205.5429
8. A logical analysis of the generalized Banach contractions principle.
   Submitted.
9. On idempotent ultrafilters in higher-order reverse mathematics.
   Preprint. arXiv:1208.1424
10. Program extraction for 2-random reals.
    Submitted.

• Der Satz von Ramsey für Paare und beweisbar rekursive Funktionen.
  Diploma Thesis (in German) supervised by Ulrich Kohlenbach, February 2009.
• Proof-mining and combinatorics: Program extraction for Ramsey's theorem for pairs.
  PhD Thesis, May 2012.

Talks:

• Ramsey's Theorem for pairs and provably recursive functions. [SLIDES]
  Contributed talk at the ASL Logic Colloquium, Sofia, Bulgaria, August 2009.
  Abstract published in: Bull. Symbolic Logic 16, no. 1, p. 121 (2010).
• Ramsey's Theorem for pairs and provably recursive functions. [SLIDES]
  Talk at the RaTLoCC 2009 - Ramsey Theory in Logic, Combinatorics and Complexity, Bertinoro, Italy, October 2009.
  
• Ramsey's theorem for pairs and program extraction. [SLIDES]
  Talk at the AMS-ASL Special Session on Logic and Analysis at the Joint Mathematics Meetings, New Orleans, January 2011.
  Abstract published in: Abstracts of Papers Presented to the Amer. Math. Soc. vol. 32, no. 1, issue 163, p. 15 (2011).
• Ramsey's Theorem for pairs and term extraction. [SLIDES]
  Talk at the RaTLoCC 2011 - Ramsey Theory in Logic, Combinatorics and Complexity, Bertinoro, Italy, May 2011.
  
• The cohesive principle and the Bolzano-Weierstraß principle. [SLIDES]
  Informal presentation at the CiE 2011, Sofia, Bulgaria, June-July 2011.
  
• The Bolzano-Weierstraß principle and the cohesive principle. [SLIDES]
  Talk at the Dagstuhl Seminar 11411: Computing with Infinite Data, October 2011.
  Abstract published in: Dagstuhl Report, Volume 1, Issue 10.
• Program extraction and Ramsey's theorem for pairs. [SLIDES]
  Talk at the Oberwolfach Workshop 1145: Mathematical Logic: Proof Theory, Constructive Mathematics, November 2011.
  Abstract published in: Oberwolfach Report No. 52/2011.
• From Bolzano-Weierstraß to Arzelà-Ascoli. [SLIDES]
  Informal presentation at Continuity, Computability, Constructivity - From Logic to Algorithms '12, Trier, Germany, May 2012.
• Non-principal ultrafilters, program extraction and higher order reverse mathematics. [SLIDES]
  Contributed talk at the Logic Colloquium 2012, Manchester, UK, July 2012.
• Non-principal ultrafilters, program extraction and higher order reverse mathematics. [SLIDES]
  Talk at the PhD Colloquium of the Colloquium Logicum 2012, Paderborn, Germany, September 2012.

Teaching:

• Summer term 2010: Assistant for Formale Grundlagen der Informatik I+II (Foundations of computer science: automata theory and logic).
• Summer term 2011: Assistant for Formale Grundlagen der Informatik I+II (Foundations of computer science: automata theory and logic).
• Summer term 2012: Assistant for Formale Grundlagen der Informatik I+II [LINK I] [LINK II] (Foundations of computer science: automata theory and logic).