  We develop NF set theory using intuitionistic logic; we call this theory INF.
We develop the theories of finite sets and their power sets, finite cardinals
and their ordering, cardinal exponentiation, addition, and multiplication. We
follow Rosser and Specker with appropriate constructive modifications,
especially replacing "arbitrary subset" by "separable subset" in the
definitions of exponentiation and order. It is not known whether \INF\ proves
that the set of finite cardinals is infinite, so the whole development must
allow for the possibility that there is a maximum integer; arithmetical
computations might "overflow" as in a computer or odometer, and theorems about
them must be carefully stated to allow for this possibility. The work presented
here is intended as a substrate for further investigations of INF.
