In intuitionistic analysis, Brouwer’s Continuity Principle implies, together with an Axiom of Countable Choice, that the positively Borel sets form a genuinely growing hierarchy: every level of the hierarchy contains sets that do not occur at any lower level.
Wim Veldman. "The Borel Hierarchy Theorem from Brouwer’s intuitionistic perspective." J. Symbolic Logic 73 (1) 1 - 64, March 2008. https://doi.org/10.2178/jsl/1208358742