Separation of analytic sets by rectangles of low complexity

Abstract

We provide Hurewicz tests for the separation of disjoint analytic sets by rectangles of the form

A Separation Result for Countable Unions of Borel Rectangles

“…His technique cannot be extended to higher levels. However, the relation just mentioned is much stronger than in [15], as we will see. The main results in this article generalize these two Zamora results, and are, hopefully, steps towards the generalization of Theorem 1.5, and then Theorem 1.4.…”

“…. This last question has been studied in [15] in the case of one rectangle. In [15], the author characterizes when two disjoint analytic sets can be separated by a Σ 0 1 (or Π 0 when ≤ 2) rectangle.…”

“…This last question has been studied in [15] in the case of one rectangle. In [15], the author characterizes when two disjoint analytic sets can be separated by a Σ 0 1 (or Π 0 when ≤ 2) rectangle. Louveau suggested that it could be very interesting to study the nonsymmetric version of the problem to understand it better (we can also make this remark for countable unions of rectangles, which is another motivation for Theorem 1.6 to come).…”