Analysis in J2
Abstract
This is an expository paper in which I explain how core mathematics, particularly abstract analysis, can be developed within a concrete countable set J2 (the second set in Jensen's constructible hierarchy). The implication, well-known to proof theorists but probably not to most mainstream mathematicians, is that ordinary mathematical practice does not require an enigmatic metaphysical universe of sets. I go further and argue that J2 is a superior setting for normal mathematics because it is free of irrelevant set-theoretic pathologies and permits stronger formulations of existence results.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.