A SEPARATION RESULT FOR COUNTABLE UNIONS OF BOREL RECTANGLES

Abstract

AbstractWe 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.