[FOM] Truth and set Theory
John Bell
jbell at uwo.ca
Thu Dec 6 14:31:47 EST 2007
Re: Truth and set theory
In Mostowski's paper, "Some impredicative definitions in the axiomatic
set-theory"
Fund. Math. 37, (1950). 111-124, it is shown that a truth definition for ZF
can be formulated within NBG but that the scheme (*) "every theorem of ZF is
true" cannot be proved in NBG (assuming the consistency of the latter). The
truth definition involves an existential quantification over classes and is
hence "impredicative". Mostowski also shows that the unprovability of (*) in
NBG is the result of a failure of induction for a certain predicate over the
natural numbers involving a bound class variable.
-- John Bell
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