A classification of ordinals up to Borel isomorphism
Volume 198 / 2008
Fundamenta Mathematicae 198 (2008), 61-76
MSC: Primary 03E10, 54H05; Secondary 03E60, 06F30.
DOI: 10.4064/fm198-1-3
Abstract
We consider the Borel structures on ordinals generated by their order topologies and provide a complete classification of all ordinals up to Borel isomorphism in $\mathsf {ZFC}$. We also consider the same classification problem in the context of $\mathsf {AD}$ and give a partial answer for ordinals $\leq\omega_2$.
