Independently Axiomatizable L_{omega_1,omega} Theories
Logic
2010-12-16 v1
Abstract
In partial answer to a question posed by Arnie Miller (http://www.math.wisc.edu/~miller/res/problem.pdf) and X. Caicedo, we obtain sufficient conditions for an L_{omega_1,omega} theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every L_{omega_1,omega} theory in a countable language has an independent axiomatization. The second, this time outright in ZFC, every intersection of a family of Borel sets can be formed as the intersection of a family of independent Borel sets.
Keywords
Cite
@article{arxiv.1012.3422,
title = {Independently Axiomatizable L_{omega_1,omega} Theories},
author = {Greg Hjorth and Ioannis Souldatos},
journal= {arXiv preprint arXiv:1012.3422},
year = {2010}
}
Comments
16 pages, no figures