FOM: Large cardinals and combinatorics

Joseph Shoenfield jrs at
Mon Mar 30 17:17:09 EST 1998

     Two replies to my recent message on the above subject state that I
failed to distinguish finite combinatorics from infinite combinatorics.
I would be much more impressed with this reply if it included a
reasonable syntactic definition of "finite combinatorial statement"
which included Harvey's principles but not Erdos's.   I would be still
more impressed if one could show that these finite combinatorial
statements had some absoluteness properties not shared by Erdos's
results.   (Please take this as a challenge, not a criticism.)

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