[FOM] The applicability of forcing
joeshipman@aol.com
joeshipman at aol.com
Wed May 2 17:24:48 EDT 2007
"Forcing" is a general term for certain kinds of arguments used in
establishing the consistency of propositions with base theories; but I
don't recall a seeing clear delineation of what is, and what is not, a
forcing argument. In order to clarify this, I ask for examples of the
following:
1) a well-known use of forcing to establish the independence of a
theorem of ZF from a weaker system than ZF
2) a well-known use of forcing which does not conform to the pattern
"Proposition D is relatively consistent with ZF plus a subset of
{A,B,C}" where A is consistent with ZFC, B is a large cardinal axiom, C
is the axiom of choice
3) a well-known independence result which was first proved by forcing,
but which can be proved "without using forcing" in some reasonable sense
4) a well-known result of the form "Proposition X is consistent with
and independent of ZFC" where neither side of the result uses forcing
-- JS
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