[FOM] definition of N without quantifying over infinite sets
T.Forster at dpmms.cam.ac.uk
Mon Aug 9 00:13:20 EDT 2004
The significance of FFF - Friedman's Finite
Form of Kruskl's theorem is of course that it is a fct about N probable
only by reasoning about infinite sets.
When explaining this to my students I of course have to anticipate that
the inductive definition of N involves quantifying over ininite sets -
after all if you contain 0 and are closed under S then you are infinite,
so i employ a definition that i learned from Quine: set theory and it
logic. You are a natural number iff every set containing you and closed
under predecessor contins 0. This doesn't involve quantification over
Did Quine invent this? If not, who did?
www.dpmms.cam.ac.uk/~tf; 01223-337981 and 020-7882-3659
More information about the FOM