[FOM] cofinite quantifier (fwd)
Thomas Forster
T.Forster at dpmms.cam.ac.uk
Wed Feb 25 10:57:16 EST 2004
This has been much on my mind recently, for several reasons. For
example, this afternoon, the man two doors away from me mentioned
that for every epsilon, it is true for cofinitely many $n$ that
there is a prime between n and n + n^{0.5 + epsilon}. Number
theory is full of assertions with this kind of flavour. Sounds
as if it would be easier if we had the cofinite quantifier as
primitive. This reminded me of a factoid Adrian Mathias told
me years ago: the theory of Turing degrees expressed with the
measure-one quantifier is decidable. How undecidable is the
theory of natural numbers with the cofinite quantifier? Does
anyone know about this?
Thomas
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