Hello, I'm Alexander! I am interested in mathematics and AI alignment. I work in Samson Abramsky's group at UCL. Outside of graduate school, I serve as Chief Bard at Timaeus.
email: a.f.d.a.FirstSurnameSecondSurname@gmail.com
Twitter: @FellowHominid
Other writing can be found at my LessWrong account - see my new shortform and my old shortform
A proof of Gödel's incompleteness theorems after A. Joyal is given. The proof uses internal category theory in an arithmetic universe, a predicative generalisation of topoi. A proof of Löb's Theorem using similar techniques is discussed.
We give an introduction to mono-Anabelian geometry, the study of what features of a scheme may be recovered from its etale fundamental group. We treat the case of the reconstruction of the base field of a curve of strictly Belyi type from its fundamental group.