Welcome to my web-page. My research interests are phase transitions in incompleteness phenomena. To read more on 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
Some short and simple examples of phase transitions in logic:
A phase transition for Dickson's lemma
A phase transition for growing trees
(2008) A phase transition for unordered regressive ramsey numbers
(2009) Unprovability of Maclagan in two variables
(2012) On the lengths of bad sequences of monomial ideals over polynomial rings, Fundamenta Mathematicae volume 216 number 2.
(2015) Monomial ideals and independence of I\Sigma_2, in press at Mathematical Logic Quarterly.
(2015) Independence of Ramsey theorem variants using \epsilon_0, joint with Harvey Friedman, Proc. Amer. Math. Soc. 144 (2016).
Latest version on the PAMS website.
The slides of my CTFM2013 talk about a part of this paper
(2013) Phase Transition Results for Three Ramsey-Like Theorems, containing a sharp phase transition for the finite adjacent Ramsey theorem, is in press at the NDJFL.
Latest version on the NDJFL website.
Improved upper bounds lemmas.
draft (2015) Dickson's lemma and Weak Ramsey, joint work with Yasuhiko Omata.
draft (2015) On the finitary Ramsey's theorem
Ongoing research: generalising phase transitions, concrete independence. Some interesting websites from general science:
How to write mathematics
My other interests:
Contact details: pelupessy (at) cage.ugent.be