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VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20251022T153951Z
DTSTART:20251029T150000Z
DTEND:20251029T160000Z
SUMMARY:Logic Seminar - Anna Dmitrieva
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}nyf-mggdrhx
 m-n0r3fw
DESCRIPTION:Speaker: Anna Dmitrieva (University of Manchester)\n\nQuasimi
 nimality and generic functions\n\nOne of the well-known accomplishments 
 of model theory is the study of the field of complex numbers\, axiomatiz
 ed by the theory of algebraically closed fields of characteristic zero. 
 It possesses numerous nice properties\, including strong minimality and 
 uncountable categoricity. However\, adding the exponential map to the st
 ructure makes it possible to define the ring of integers\, preventing fi
 rst-order axiomatization and many other properties. Nevertheless\, there
  is still hope that the complex exponential field can be successfully st
 udied using higher-order logic and\, in particular\, that it is quasimin
 imal\, i.e. every definable subset is countable or co-countable.\n\nIn 2
 002 Zilber introduced the theory of a generic function\, which is a firs
 t-order theory axiomatizing a function on an algebraically closed field 
 of characteristic zero that satisfies versions of the Schanuel property 
 and existential closedness. This theory possesses many nice properties\,
  analogous to the ones we expect from the complex exponential field.  As
  the main result\, we prove that adding an entire generic function to th
 e complex field gives a quasiminimal structure\, and\, moreover\, this s
 tructure is unique up to an isomorphism.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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