A coanalytic set is a definable set which is the complement of an analytic set.
Assuming the axiom of constructibility 
for the constructible
universe, Wang (2026) proved that for every ![alpha in [0,1]](/images/equations/CoanalyticSet/Inline2.svg)
there is a coanalytic proper subfield
of 
with Hausdorff
dimension 
.
These subfields can be chosen as a strictly increasing
family 
with 
.
These subfields need not be Borel
sets. This gives a conditional construction related to Erdős
problem 1154; it does not settle
the unrestricted question in ZFC. Wang (2026) acknowledges Danus assistance with
proof search and development.
