  We analyze the "F-locality condition" (proposed by Kay to be a mathematical
implementation of a philosophical bias related to the equivalence principle, we
call it the "GH-equivalence principle"), which is often used to build a
generalization of quantum field theory to non-globally hyperbolic spacetimes.
In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to
the effect that time machines with compactly generated Cauchy horizons are
incompatible with the F-locality condition actually does not support the
"chronology protection conjecture", but rather testifies that the F-locality
condition must be modified or abandoned. We also show that this condition
imposes a severe restriction on the geometry of the world (it is just this
restriction that comes into conflict with the existence of a time machine),
which does not follow from the above mentioned philosophical bias. So, one need
not sacrifice the GH-equivalence principle to "emend" the F-locality condition.
As an example we consider a particular modification, the "MF-locality
condition". The theory obtained by replacing the F-locality condition with the
MF-locality condition possesses a few attractive features. One of them is that
it is consistent with both locality and the existence of time machines.
