Independently axiomatizable ℒω1,ω theories
Greg Hjorth and Ioannis A. Souldatos
Source: J. Symbolic Logic
Volume 74, Issue 4
(2009), 1273-1286.
Abstract
In partial answer to a question posed by Arnie Miller [4] and X. Caicedo [2] we obtain sufficient conditions for an ℒω1,ω theory to have an independent axiomatization. As a consequence we obtain two corollaries: The first, assuming Vaught's Conjecture, every ℒω1,ω 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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1254748691
Digital Object Identifier: doi:10.2178/jsl/1254748691
Mathematical Reviews number (MathSciNet):
MR2518564
References
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Mathematical Reviews (MathSciNet):
MR619449
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Mathematical Reviews (MathSciNet):
MR177873
