Journal of Symbolic Logic

Independently axiomatizable ℒω1 theories

Greg Hjorth and Ioannis A. Souldatos

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Abstract

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

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

Dates
First available in Project Euclid: 5 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1254748691

Digital Object Identifier
doi:10.2178/jsl/1254748691

Mathematical Reviews number (MathSciNet)
MR2518564

Citation

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. https://projecteuclid.org/euclid.jsl/1254748691


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