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FAILURES OF THE SILVER DICHOTOMY IN THE GENERALIZED BAIRE SPACE

  • SY-DAVID FRIEDMAN (a1) and VADIM KULIKOV (a1)

Abstract

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

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[1]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.
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[3]Halko, A. and Shelah, S.. On strong measure zero subsets of κ2. Fundamenta Mathematicae, vol. 170 (2001), pp. 219229.
[4]Kulikov, V.. Borel reductions in the generalised Cantor space, this Journal, vol. 78 (2013), no. 2, pp. 439458.
[5]Lücke, P.. ${\rm{\Sigma }}_1^1 $-definability at uncountable regular cardinals, this Journal, vol. 77 (2012), no. 3, pp. 10111046.
[6]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.

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FAILURES OF THE SILVER DICHOTOMY IN THE GENERALIZED BAIRE SPACE

  • SY-DAVID FRIEDMAN (a1) and VADIM KULIKOV (a1)

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