[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.


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