BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anna Dmitrieva (UEA) DTSTART:20241119T140000Z DTEND:20241119T150000Z DTSTAMP:20260421T154237Z UID:UEAPS/44 DESCRIPTION:Title: G eneric functions and quasiminimality\nby Anna Dmitrieva (UEA) as part of ANTLR seminar\n\n\nAbstract\nOne of the well-known accomplishments of m odel theory is the study of the field of complex numbers. It possesses num erous nice properties\, including minimality\, i.e. any definable subset i s finite or cofinite. However\, adding the exponential map to the structur e makes it possible to define the ring of integers\, preventing minimality and many other properties. Nevertheless\, there is still hope that the co mplex exponential field is somewhat well-behaved. For instance\, Zilber’ s quasiminimality conjecture states that the complex exponential field is quasiminimal\, i.e. every definable subset is countable or co-countable. A nalogous conjectures were made\, replacing the exponential map with other analytical functions.\n\nIn this talk we look at the theory of a generic f unction\, as introduced by Zilber in 2002. As the main result\, we prove t hat adding an entire generic function to the complex field gives a quasimi nimal structure\, and\, moreover\, this structure is unique up to an isomo rphism. Thus we obtain a non-trivial example of an entire function which k eeps the complex field quasiminimal.\n LOCATION:https://researchseminars.org/talk/UEAPS/44/ END:VEVENT END:VCALENDAR