[FOM] Koenigsmann's universal definition of Z in Q

[Timothy Y. Chow]

Something else worth mentioning, that I noticed when looking at 
Koenigsmann's paper a little more carefully, is that his theorem has been 
generalized by Jennifer Park to arbitrary number fields.

   J. Park, "A universal first-order formula defining the ring of
   integers in a number field," Math. Res. Lett. 20 (2013), 961-980.

Park's proof makes use of some heavier-duty number theory---global class 
field theory in particular.  Park also notes, "The proofs that follow are 
further aided by a theorem, proved and communicated by Tate, which allows 
one to find an element x in K that has prescribed Hilbert symbols against 
finitely many elements of K.  The special case where K = Q is well-known; 
for example, see [Serre's Course in Arithmetic], Theorem 4, page 24, but 
the general case of K being a global field does not appear in the 
literature."

Tim