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SUMMARY:A universal first-order formula for the ring of integers inside a 
 number field
DTSTART:20120809T111500
DTEND:20120809T123000
DTSTAMP:20260916T043438Z
UID:6ab02f2614c8baca6e3fa6602d634b210b988e396d3e5c0bc978f29b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jennifer Park\nHilbert's tenth problem over Q (or\, any number
  field K) asks the following: given a polynomial in several variables with
  coefficients in Q (resp. K)\, is there a\ngeneral algorithm that decides 
 whether this polynomial has a solution in Q (resp. K)? Unlike the classica
 l Hilbert's tenth problem over Z\, this problem is still open.\nTo reduce 
 this problem to the classical problem\, we need a definition of Z in Q (re
 sp. ring of integers in K) using only an existential quantifier. This prob
 lem is\nstill open. I will present a definition of the ring of integers in
  a number field\, which uses only one universal quantifier\, which is\, in
  a sense\, the simplest logical\ndescription that we can hope for. This is
  a generalization of Koenigsmann's work\, which defines Z in Q using one u
 niversal quantifier.\n
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 nem
STATUS:CONFIRMED
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