Alexander P. Kreuzer's homepage

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I am a machine learning/artificial intelligence professional with a strong background in theoretical computer science and mathematical logic.

Below you can find information on my research. My primary research interest are proof theory, computability theory, and formal methods.

Until July 2016 I was a research fellow in the mathematics department of National University of Singapore working together with Chi Tat Chong, Frank Stephan, and Yang Yue.

Prior to that I was a postdoc in the Plume team at Laboratoire de l'Informatique du Parallélisme, École normale supérieure de Lyon under Colin Riba and Alexandre Miquel.

I received my PhD in April 2012 from the Mathematics Department of Technische Universität Darmstadt under the supervision of Prof. Ulrich Kohlenbach.


Contact:

Email: matkaps [at] posteo [dot] de

Publications:

  1. On the Uniform Computational Content of the Baire Category Theorem (with Vasco Brattka, and Matthew Hendtlass).
    Accepted for publication in the Notre Dame Journal of Formal Logic. arXiv:1510.01913.
  2. On the Uniform Computational Content of Computability Theory (with Vasco Brattka, and Matthew Hendtlass).
    Submitted. arXiv:1501.00433.
  3. Measure theory and higher order arithmetic.
    Final version in: Proc. Amer. Math. Soc. 143 (2015), 5411-5425.
    Preprint available at arXiv:1312.1531.
    [doi:10.1090/proc/12671] [MR 3411156]
  4. Bounded variation and the strength of Helly's selection theorem.
    Final version in: LMCS Vol. 10(4:16) 2014.
    [doi:10.2168/LMCS-10(4:16)2014] [MR 3296477]
  5. On principles between Σ1- and Σ2-induction, and monotone enumerations (with Keita Yokoyama).
    Final version in: J. of Mathematical Logic 16, 1650004 (2016).
    Preprint available at arXiv:1306.1936.
    [doi:10.1142/S0219061316500045]
  6. Minimal idempotent ultrafilters and the Auslander-Ellis theorem.
    Preprint. arXiv:1305.6530.
  7. Program extraction for 2-random reals.
    Final version in: Archive for Mathematical Logic, vol. 52 (2013), no. 5-6, 659-666.
    [doi:10.1007/s00153-013-0336-9] [MR 3072783]
  8. On idempotent ultrafilters in higher-order reverse mathematics.
    Final version in: J. of Symbolic Logic vol. 80 (2015), no. 1, pp. 179-193.
    Preprint available at arXiv:1208.1424.
    [doi:10.1017/jsl.2014.58] [MR 3320588]
  9. A logical analysis of the generalized Banach contractions principle.
    Final version in: Journal of Logic & Analysis, vol. 4 (2012), 17.
    [MR 3002655]
  10. From Bolzano-Weierstraß to Arzelà-Ascoli.
    Final version in: Mathematical Logic Quarterly, vol. 60 (2014), no. 3, pp. 177-183
    Preprint available at arXiv:1205.5429.
    [doi:10.1002/malq.201200076] [MR 3207207]
  11. Non-principal ultrafilters, program extraction and higher order reverse mathematics.
    Final version in: J. of Mathematical Logic, vol. 12 (2012), no 1.
    Preprint available at arXiv:1109.4277. Updated preprint.
    [doi:10.1142/S021906131250002X] [MR 2950192]
  12. On the strength of weak compactness.
    Final version in: Computability, vol. 1 (2012), no. 2, 171-179.
    Preprint available at arXiv:1106.5124. Updated preprint.
    [doi:10.3233/COM-12010] [MR 3064228]
  13. 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] [MR 2925280]
  14. Term extraction and Ramsey's theorem for pairs (with Ulrich Kohlenbach).
    Final version in: J. of Symbolic Logic vol. 77 (2012), no. 3, pp. 853-895.
    [doi:10.2178/jsl/1344862165] [MR 2987141]
  15. The cohesive principle and the Bolzano-Weierstraß principle.
    Final version in: Mathematical Logic Quarterly, vol. 57 (2011), no. 3, pp. 292-298.
    Preprint available at arXiv:1005.5316.
    [doi:10.1002/malq.201010008] [MR 2839129]
  16. 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]

Research notes et cetera:

Talks:

Teaching at National University of Singapore:

  • 2015/2016, Semester 1: MA5219 Logic and Foundations of Mathematics.

Teaching at TU Darmstadt: