[FOM] definition of N without quantifying over infinite sets
Thomas Forster
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
infinite sets.
Did Quine invent this? If not, who did?
Thomas Forster
www.dpmms.cam.ac.uk/~tf; 01223-337981 and 020-7882-3659
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