[FOM] Set theory as a revealer

[Wim Mielants]

  Some interesting theorems about braids have been revealed by the large
cardinal hypothesis I3 (the existence of self simular ranks)
Laver,Steel and Dehornoy have proved that I3 implies the acyclicity of
divisibility of the free system where the self distibutivity identity
x.(y.z)=(xy).(xz) holds,and this implies the existence of a certain
ordening on braids which gives a new solution for the isotopy problem of
braids and also for many other questions obout braids (see;Braids and
Self-Distributivity of Patrick Dehornoy,Birkhauser Verlag 2000)
  Dehornoy has then found a proof of this theorem without the I3
hypothesis,using braidgroups,but there exist a large gap of complexity
between the two proofs.It was set theory which has given the technical
framework for formalising the initial intuition (self- simular sets)and
has offered the tools(ranks,ordinals)that have allowed to discover the
properties that were included and somehow hidden (the acyclicity property
of self-distributive systems).
   Dehornoy remarks that set theory works in this case as a photographic
film:it reveals new phenomens without having a real connection with them.

    My question is:are there other phenomens known in mathematics wich are
revealed in such a way by set theory,or is this result an exception?

                          Wim Mielants.