FOM: Friedman's independence results, an epochal f.o.m. advance

Torkel Franzen torkel at
Fri Mar 13 08:19:01 EST 1998

  Steve Simpson says:

  >I would like to call attention to Harvey Friedman's posting

  >       FOM: 12:Finite trees/large cardinals

  >of 11 Mar 1998 11:36:36.  It represents tremendously important
  >progress in f.o.m.

  This may well be the case, but remains to be established, at least
if f.o.m. is to be a subject of interest to non-specialists.

  My own tendency as I attempt to penetrate the combinatorial
principles here at issue is to lapse into slack-jawed wonder that
anybody can make sense of them, let alone formulate them. No doubt
there are many other readers who comprehend them with relative ease,
but there are probably very few who have anything approaching
Friedman's peculiar ability to formulate, analyze and wrap his brain
around principles of this type. What is needed to convince people
that these are "very natural combinatorial propositions" is to find
some striking applications of them. Even I could no doubt grasp
these principles if I set my mind to it, but I need some incentive.

  Also, it is a significant circumstance that the only occurrence of
the phrase "subtle cardinal" on any web page indexed by AltaVista is a
reference to Cardinal Granvelle. To establish Friedman's results as
important progress in f.o.m., a principle that yields the existence of
subtle cardinals must be established as a comprehensible and
potentially acceptable addition to the axioms of set theory.

  So without in any way seeking to belittle what is surely a remarkable
piece of work, I think it's a bit too soon to characterize it as
tremendously important progress in f.o.m.

Torkel Franzen
Computer science, Lulea technical university

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