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Independently axiomatizable ℒω1,ω theories

Published online by Cambridge University Press:  12 March 2014

Greg Hjorth  and
Ioannis A. Souldatos
Greg Hjorth
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville, Vic 3010, Australia, E-mail: [email protected]
Ioannis A. Souldatos
Affiliation:
273 Wissink Hall, Office 261 Mathematics Department, Minnesota State UniversityMankato, Mn 56001, USA, E-mail: [email protected]
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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,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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1273 - 1286
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

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