Generalizing Hartogs' Trichotomy Theorem
Logic
2008-04-07 v1
Abstract
A celebrated argument of F. Hartogs (1915) deduces the Axiom of Choice from the hypothesis of comparability for any pair of cardinals. We show how each of a sequence of seemingly much weaker hypotheses suffices. Fixing a finite number , the Axiom of Choice follows if merely any family of cardinals contains at least one comparable pair.
Keywords
Cite
@article{arxiv.0804.0673,
title = {Generalizing Hartogs' Trichotomy Theorem},
author = {David Feldman and Mehmet Orhon and Andreas Blass},
journal= {arXiv preprint arXiv:0804.0673},
year = {2008}
}
Comments
8 pages with an appendix by Andreas Blass