# No Subject


somewhere between ZFC and ZFC+SI. The lower bound is proved in
cite{grue92} by means of a syntactical translation of ZFC (including
classical propositional and predicate calculus) into map theory, and
the upper bound by building an (exceedingly complex) model of map
theory within ZFC+SI. The present paper confirms the upper bound by
providing much simpler models, the canonical models'' of the paper,
which are in fact the paradigm of a large class of quite natural
models of MT.

That all these models interpret a model of ZFC is a consequence of the
syntactic translation, which is a difficult theorem of
\cite{grue92}. We can however give here a direct proof of a stronger
result, namely that they interpret some $(V_{\sigma},{\in})$, where
$\sigma$ is an inaccessible cardinal.  Finally we return to the
canonical'' models and show that they are adequate for the notion of
computation which underlies MT.