The Strength of the Besicovitch-Davies Theorem [chapter]

Bjørn Kjos-Hanssen, Jan Reimann
2010 Lecture Notes in Computer Science  
A theorem of Besicovitch and Davies implies for Cantor space 2 ω that each Σ 1 1 (analytic) class of positive Hausdorff dimension contains a Π 0 1 (closed) subclass of positive dimension. We consider the weak (Muchnik) reducibility ≤w in connection with the mass problem S(U ) of computing a set X ⊆ ω such that the Σ 1 1 class U of positive dimension has a Π 0 1 (X) subclass of positive dimension. We determine the difficulty of the mass problems S(U ) through the following results:
doi:10.1007/978-3-642-13962-8_26 fatcat:3vm2icfh7neztcc4cbuqzcau3m