2 results
THE GAME OPERATOR ACTING ON WADGE CLASSES OF BOREL SETS
-
- Journal:
- The Journal of Symbolic Logic / Volume 84 / Issue 3 / September 2019
- Published online by Cambridge University Press:
- 13 June 2019, pp. 1224-1239
- Print publication:
- September 2019
-
- Article
- Export citation
-
We study the behavior of the game operator
$$ on Wadge classes of Borel sets. In particular we prove that the classical Moschovakis results still hold in this setting. We also characterize Wadge classes 
${\bf{\Gamma }}$ for which the class 
has the substitution property. An effective variation of these results shows that for all 
$1 \le \eta < \omega _1^{{\rm{CK}}}$ and 
$2 \le \xi < \omega _1^{{\rm{CK}}}$, 
is a Spector class while 
is not.
A SEPARATION RESULT FOR COUNTABLE UNIONS OF BOREL RECTANGLES
-
- Journal:
- The Journal of Symbolic Logic / Volume 84 / Issue 2 / June 2019
- Published online by Cambridge University Press:
- 22 February 2019, pp. 517-532
- Print publication:
- June 2019
-
- Article
- Export citation
-
We provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a countable union of
${\bf{\Sigma }}_1^0 \times {\bf{\Sigma }}_\xi ^0$ sets, or by a 
${\bf{\Pi }}_1^0 \times {\bf{\Pi }}_\xi ^0$ set.
