Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-19T04:30:50.996Z Has data issue: false hasContentIssue false

FAILURES OF THE SILVER DICHOTOMY IN THE GENERALIZED BAIRE SPACE

Published online by Cambridge University Press:  22 April 2015

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

Abstract

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

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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. 219229.CrossRefGoogle Scholar
Kulikov, V.. Borel reductions in the generalised Cantor space, this Journal, vol. 78 (2013), no. 2, pp. 439458.Google Scholar
Lücke, P.. ${\rm{\Sigma }}_1^1 $-definability at uncountable regular cardinals, this Journal, vol. 77 (2012), no. 3, pp. 10111046.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. 10521070.Google Scholar