FOM: Large Cardinals and Combinatorics

Joseph Shoenfield jrs at
Thu Mar 26 15:56:44 EST 1998

     The recent debate over the epochal significance of Harvey's 
results seems to ignore the history of set thery.   These results show
that large cardinals can be used to prove combinatorial principles
not provable in ZFC.   Such results were obtained by Erdos and his
colloaborators in the sixties.   The combinatorial principles were
infinite generalizations of well-known results in finite combinatorics.
These results were not of much interest to logicians until Rowbottom
discovered that they could be use to prove significant facts about
constructible sets.   Rowbottom's result were considerably extended
by Silver in his thesis; these techniques have become a standard tool
in the study of core models.   Harvey's results may be different in
some respects from these results, but hardly of epochal significance.

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