This site remains under construction, latest update: November 2016
Find my blog here.
Welcome to my web-page. I am a foreign post-doctoral researcher at Tohoku University. 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.
- Draft (2016) On \alpha-largeness and the Paris--Harrington principle in RCA_0 and RCA_0^*.
- Draft (2016) Reverse mathematics of the finite downwards closed subsets of \N^k ordered by inclusion. (Submitted)
- Draft (2016) Reverse mathematics of the relativised fast growing hierarchy.
(2016) Independence of Ramsey theorem variants using \epsilon_0, joint with Harvey Friedman, Proc. Amer. Math. Soc. 144 (2016).
The slides of my CTFM2013 talk about a part of this paper.
- Draft (2015) On the finitary Ramsey's theorem.
- Draft (2015) Dickson's lemma and Weak Ramsey, joint work with Yasuhiko Omata.
- (2015) Monomial ideals and independence of I\Sigma_2, in press at Mathematical Logic Quarterly.
(2013) Phase Transition Results for Three Ramsey-Like Theorems, Notre Dame Journal of Formal Logic, issue 57.2 (2016).
Improved upper bounds lemmas.
- (2012) On the lengths of bad sequences of monomial ideals over polynomial rings, joint work with Andreas Weiermann, Fundamenta Mathematicae volume 216 number 2.
- (2009) Unprovability of Maclagan in two variables, joint work with Andreas Weiermann.
- (2008) A phase transition for unordered regressive ramsey numbers, joint work with Andreas Weiermann.
Some interesting websites about science