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FAILURES OF THE SILVER DICHOTOMY IN THE GENERALIZED BAIRE SPACE

Published online by Cambridge University Press:  22 April 2015

SY-DAVID FRIEDMAN  and
VADIM KULIKOV
SY-DAVID FRIEDMAN
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITY OF VIENNA WÄHRINGER STRASSE 25, 1090, VIENNA, AUSTRIA
VADIM KULIKOV
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITY OF VIENNA WÄHRINGER STRASSE 25, 1090, VIENNA, AUSTRIA
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Abstract

We prove results that falsify Silver’s dichotomy for Borel equivalence relations on the generalized Baire space under the assumption V = L.

Keywords

03E1503E35Generalized Desriptive Set TheoryGeneralized Baire spaceSilver dichotomyGeneralized Borel Reducibility
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 2 , June 2015 , pp. 661 - 670
Copyright
Copyright © The Association for Symbolic Logic 2015 

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References

REFERENCES

Friedman, S. D., Hyttinen, T., and Kulikov, V.. Generalized descriptive set theory and classification theory. Memoirs of the American Mathematical Society, vol. 230 (2014), no. 1081.Google Scholar
Halko, A.. Negligible subsets of the generalized Baire space $\omega _1^{\omega _1 } $. Annales Academiae Scientiarum Series Mathematica. Dissertationes, no. 107 (1996).Google Scholar
Halko, A. and Shelah, S.. On strong measure zero subsets of κ2. Fundamenta Mathematicae, vol. 170 (2001), pp. 219–229.CrossRefGoogle Scholar
Kulikov, V.. Borel reductions in the generalised Cantor space, this Journal, vol. 78 (2013), no. 2, pp. 439–458.Google Scholar
Lücke, P.. ${\rm{\Sigma }}_1^1 $-definability at uncountable regular cardinals, this Journal, vol. 77 (2012), no. 3, pp. 1011–1046.Google Scholar
Mekler, A. and Väänänen, J.. Trees and ${\rm{\Pi }}_1^1 $-subsets of ${}_{}^{\omega _1 } \omega _1^{} $, this Journal, vol. 58 (1993), no. 3, pp. 1052–1070.Google Scholar