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Borel structures and Borel theories

Published online by Cambridge University Press:  12 March 2014

Greg Hjorth  and
André Nies
Greg Hjorth
Affiliation:
Department of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia
André Nies
Affiliation:
Department of Computer Science, Auckland University, Auckland, New Zealand, E-mail: andre@cs.auckland.ac.nz
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Abstract

We show that there is a complete, consistent Borel theory which has no “Borel model” in the following strong sense: There is no structure satisfying the theory for which the elements of the structure are equivalence classes under some Borel equivalence relation and the interpretations of the relations and function symbols are uniformly Borel.

We also investigate Borel isomorphisms between Borel structures.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 461 - 476
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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