I like, in maths, proof theory, large cardinals, inner model theory, recursion theory, and in computer science, cryptography and operating systems development.
My preprints and notes
I have so far published 2 preprints. I shall keep a repository of all my papers, as well as their LaTeX source code, on this website.
This paper serves to define an extension, which we call dimensional Veblen, of Oswald Veblen's system of ordinal functions below the large Veblen ordinal. This is facilitated by iterating derivatives of ordinal functions along multidimensional array structures, and can be viewed as the "maximal" natural extension of the Veblen functions. We then construct an ordinal notation based on it, and provide a conversion algorithm from Buchholz's function below the Bachmann-Howard ordinal.
ArXiV identifier: 2310.12832. The version available there also has minor typo fixes.
We share both recent and older, well-known results regarding the notions of stable ordinals and shrewd cardinals. We then argue that \(\Sigma_2\)-nonprojectible ordinals may be considered as recursive analogues to subtle cardinals, a highly combinatorial type of cardinal related to Jensen's fine structure, due to the latter possessing a characterisation in terms of shrewdnesss.
ArXiV identifier: 2312.15818.
I have not published any sets of notes regarding courses or particular topics.
Talks
“Stability, interpretability and nonprojectibility” (contributed talk, European Set Theory Conference 2024)
In this talk I discuss my theorem that \(\Sigma_2\)-nonprojectility can be considered analogous to subtlety; formally, that a notion which many would agree encapsulates the strength of subtlety is in fact equivalent to \(\Sigma_2\)-nonprojectibility. I therefore focus on two polar opposites in the ordinals: countable ordinals and large cardinals. We consider analogies in the structure of these. Kranakis, Richter, Aczel, Klev, Rathjen & Kaufmann have in the past discussed countable analogues to large cardinals and the difficulty of formalizing such a general notion. As part of my case I share some previously known results on the structure of stable ordinals and an equivalence of subtle cardinals (a combinatorial principle) with a significant strengthening of indescribability.
”(\mathcal{P}(\kappa)/\mathsf{NS}_\kappa) and Stationary Reflection” (contributed talk, Set Theory in the UK 17)
My favourite languages are C, due to its simplicity and versatility, and Rust, due to its conceptual elegance. I used to use C++, but switched after growing disillusioned with OOP. For simple scripting, I like Python. I know a small amount of C#, Go and JavaScript.
Below are .tar.gz archives, for projects containing multiple files and a lot of data or code, created through tar -zcvf. I’ve also attached SHA-256 sums, to ensure you’re not downloading a corrupted PDF.
A tarball of the Dimensional Veblen PDF, bibliography and source code: dimveb.tar.gz (sha256).
A tarball of the recursive analogues PDF, bibliography and source code: recanalogue.tar.gz (sha256).
Somewhat extraneous facts
I’m a proud member of the LGBTQ+ community.
My Myers-Briggs personality type is INTP-T.
I live in the UK and speak English fluently (C2), and I used to speak German natively since I was born in Germany.