Articles and Preprints

• Dickson’s lemma and Weak Ramsey, joint work with Yasuhiko Omata, Archive for Mathematical Logic 58 (2019), doi: 10.1007/s00153-018-0642-3.

• Reverse mathematics of the finite downwards closed subsets of \(\textrm{ } \mathbb{N}^k \) 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 \( \textrm{ I}\Sigma_2 \), Mathematical Logic Quarterly 63 (2017), doi: 10.1002/malq.201500035.

• On \(\alpha\)-largeness and the Paris–Harrington principle in \( \mathrm{RCA}_0 \) and \( \mathrm{RCA}^\star_0 \), Draft (2016).

• Reverse mathematics of the relativised fast growing hierarchy, Draft (2016).

• Independence of Ramsey theorem variants using \(\varepsilon_0\), 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 Ramsey-Like Theorems, Notre Dame Journal of Formal Logic, issue 57.2 (2016), doi: 10.1215/00294527-3452807.

• 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/fm216-2-1.

• Unprovability of Maclagan in two variables, joint work with Andreas Weiermann, CiE2009.

• A phase transition for unordered regressive ramsey numbers, joint work with Andreas Weiermann, CiE2008.