We introduce ‘‘ultrafilter limits’’ into the
classical Turing model of computation and develop a paradigm for interpreting the problem of distinguishing the class P from NP as a logical problem of decidability. We use P(NP) to denote decision problems which can be solved on a (nondeterministic) Turing machine in polynomial time. The concept is that in an appropriate limit it may be possible to prove
that problems in P are still decidable, so a problem whose limit is undecidable would be established as lying outside of P.