  In this paper, we show that Markov's principle is not derivable in dependent
type theory with natural numbers and one universe. One way to prove this would
be to remark that Markov's principle does not hold in a sheaf model of type
theory over Cantor space, since Markov's principle does not hold for the
generic point of this model. Instead we design an extension of type theory,
which intuitively extends type theory by the addition of a generic point of
Cantor space. We then show the consistency of this extension by a normalization
argument. Markov's principle does not hold in this extension, and it follows
that it cannot be proved in type theory.
