Ordinal Notation

Abstract

We introduce a framework for ordinal notation systems, present a family of strong yet simple systems, and give many examples of ordinals in these systems. While much of the material is conjectural, we include systems with conjectured strength beyond second order arithmetic (and plausibly beyond ZFC), and prove well-foundedness for some weakened versions.

arXiv comment64 pages, major revision, the original html (OrdinalNotation.htm) and the accompanying code (OrdinalArithmetic.py) are in ancillary files