2 papers
math.LO2025
Reflection ranks via infinitary derivations
James Walsh
There is no infinite sequence of -sound extensions of each of which proves -reflection of the next. This engenders a well-founded ``reflection rank…
math.LO2025
On the hierarchy of natural theories
James Walsh
It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of "natural," it is…