Is forcing forced on us?

[martdowd at aol.com]

 FOM:
There are independent questions which can be shown to be independent
via large cardinal axioms, without the need for forcing.  The most fundamental
example is V=L.  The most basic generic extension falsifies it.
Assuming a measurable cardinal does also.  There are probably other examples,
but I'ld have to do some research; maybe other FOM'ers know some off
the top of their head.
For one other example. diamond was first shown to hold in  a forcing extension,then later in L.
Shelah's dream 4.8,   Can we find a method parallel to forcing for L (i.e., for the usual
   axioms of set theory + every set is constructible)?is of interest, because if V=L then forcing is useless.  He goes on to say
   A major preliminary obstacle to this dream is the lack of a good candidate to
  be a test problem, since so many questions have already been settled under the
  assumption V = L.One possible test problem can be found in
   "A Question on Indiscernibles"   https://www.researchgate.net/publication/313588697

Martin Dowd
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