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Fσ EQUIVALENCE RELATIONS AND LAVER FORCING

Published online by Cambridge University Press:  25 June 2014

MICHAL DOUCHA
MICHAL DOUCHA*
Affiliation:
INSTITUTE OF MATHEMATICS, ACADEMY OF SCIENCES, PRAGUE, CZECH REPUBLICE-mail: m.doucha@post.cz
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Abstract

Following the topic of the book Canonical Ramsey Theory on Polish Spaces by V. Kanovei, M. Sabok, and J. Zapletal we study Borel equivalences on Laver trees. We prove that equivalence relations Borel reducible to an equivalence relation on 2ω given by some FσP-ideal on ω can be canonized to the full equivalence relation or to the identity relation.

This has several consequences, e.g., Silver type dichotomy for the Laver ideal and equivalences Borel reducible to equivalence relations given by FσP-ideals.

Keywords

03E1503E05Borel equivalence relationsLaver idealCanonical Ramsey theorem
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 2 , June 2014 , pp. 644 - 653
Copyright
Copyright © The Association for Symbolic Logic 2014 

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References

REFERENCES

Kanovei, V., Sabok, M., and Zapletal, J., Canonical Ramsey theory on polish spaces, Cambridge University Press, Cambridge, UK, 2013.Google Scholar
Solecki, S., Analytic ideals and their applications. Annals of Pure and Applied Logic, vol. 99 (1999), no. 1–3, pp. 51–72.CrossRefGoogle Scholar
Zapletal, J., Forcing idealized, Cambridge University Press, Cambridge, UK, 2008.Google Scholar