[FOM] Re:Independence without forcing
Martin Davis
martin at eipye.com
Thu Jul 10 01:02:45 EDT 2003
Todd Eisworth has asked about independence results in set theory that do
not use forcing.
Harvey Friedman has found numerous examples, mostly of a combinatorial
nature, of propositions that are provable from the existence of large (but
not very large) cardinals together with ZFC. His methods do not involve
forcing at all. He proves the equivalence of these propositions with
statements that we know (by Goedel's work) are unprovable in ZFC. The
propositions are also independent of ZFC + V=L.
One can easily track down some of these results in the FOM archive by using
the google link on the FOM information page. Try as key words: Friedman,
Boolean relation, subtle cardinals.
Martin
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