This site remains under construction, latest update: November 2018
Find my blog here.
Welcome to my webpage. My current research interests are weak concrete incompleteness phenomena, phase transitions for incompleteness, and reverse mathematics.
To read more about mathematical incompleteness I recommend Prof. Harvey Friedman's webpage, which also contains an extensive overview in the introduction of his book on Boolean Relation Theory.
For more on phase transitions: My supervisor's webpage.
This research relies heavily on results from proof theory, for a compact introduction visit Prof. Wilfried Buchholz's webpage.
The standard work for an introduction into reverse mathematics is Subsystems of Second Order Arithmetic, by Stephen G. Simpson.
Articles and preprints
 Dickson's lemma and Weak Ramsey, joint work with Yasuhiko Omata, in press at the Archive for Mathematical Logic (2018), doi: 10.1007/s0015301806423.
 Reverse mathematics of the finite downwards closed subsets of \N^k ordered by inclusion and adjacent Ramsey for fixed dimension, Mathematical Logic Quarterly 64 (2018), doi: 10.1002/malq.201700040.
 The strength of SCT soundness, joint with Emanuele Frittaion, Silvia Steila and Keita Yokoyama Journal of Logic and Computation 28 (2018), doi: 10.1093/logcom/exy003.
 Monomial ideals and independence of I\Sigma_2, Mathematical Logic Quarterly 63 (2017), doi: 10.1002/malq.201500035.
 On \alphalargeness and the ParisHarrington principle in RCA_0 and RCA_0^* , Draft (2016).
 Reverse mathematics of the relativised fast growing hierarchy, Draft (2016) .

Independence of Ramsey theorem variants using \epsilon_0, joint with Harvey Friedman, Proc. Amer. Math. Soc. 144 (2016), doi: 10.1090/proc12759
The slides of my CTFM2013 talk about a part of this paper. 
Phase Transition Results for Three RamseyLike Theorems, Notre Dame Journal of Formal Logic, issue 57.2 (2016), doi: 10.1215/002945273452807
Improved upper bounds lemmas.  On the finitary Ramsey's theorem, Draft (2015) .
 On the lengths of bad sequences of monomial ideals over polynomial rings, joint work with Andreas Weiermann, Fundamenta Mathematicae volume 216 number 2 (2012), doi: 10.4064/fm21621 .
 Preprint (2009) Unprovability of Maclagan in two variables, joint work with Andreas Weiermann, CiE2009.
 Preprint (2008) A phase transition for unordered regressive ramsey numbers, joint work with Andreas Weiermann, CiE2008.
Some interesting websites about science
David Hilbert
Scientific American
Improbable research
Appendix F
How to write mathematics
Other interests