  We make a proposal for a bosonic field theory in twelve dimensions that
admits the bosonic sector of eleven-dimensional supergravity as a consistent
truncation. It can also be consistently truncated to a ten-dimensional
Lagrangian that contains all the BPS p-brane solitons of the type IIB theory.
The mechanism allowing the consistent truncation in the latter case is unusual,
in that additional fields with an off-diagonal kinetic term are non-vanishing
and yet do not contribute to the dynamics of the ten-dimensional theory. They
do, however, influence the oxidation of solutions back to twelve dimensions. We
present a discussion of the oxidations of all the basic BPS solitons of
M-theory and the type IIB string to D=12. In particular, the NS-NS and R-R
strings of the type IIB theory arise as the wrappings of membranes in D=12
around one or other circle of the compactifying 2-torus.
