Journal of Symbolic Logic

Independently axiomatizable ℒω1 theories

Greg Hjorth and Ioannis A. Souldatos

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In partial answer to a question posed by Arnie Miller [4] and X. Caicedo [2] we obtain sufficient conditions for an ℒω1 theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every ℒω1 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.

Article information

J. Symbolic Logic, Volume 74, Issue 4 (2009), 1273-1286.

First available in Project Euclid: 5 October 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Hjorth, Greg; Souldatos, Ioannis A. Independently axiomatizable ℒ ω 1 ,ω theories. J. Symbolic Logic 74 (2009), no. 4, 1273--1286. doi:10.2178/jsl/1254748691.

Export citation