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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20240531T172642Z
DTSTART:20240605T141500Z
DTEND:20240605T153000Z
SUMMARY:Logic seminar: Pietro Freni
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}x9s-lwgdrqa
v-8x20js
DESCRIPTION:Title: T-convexity and T-lambda-spherical completions of o-mi
nimal structures.\n\nAbstract: After introducing the basic notions relev
ant to the talk (valued field\, o-minimal theory\, T-convexity)\, I will
discuss generalizations of the Kaplanski embedding theorem for RCVFs to
T-convexly valued o-minimal fields [4].\n\nIf T is power bounded\, ther
e is a known straightforward generalization: every T-convexly valued (E\
, O) has a unique-up-to-non-unique-isomorphism spherically complete imme
diate elementary extension (follows from the residue-valuation property
[3]\,[5]). This cannot happen if T is exponential [2].\n\nHowever\, the
following generalization still holds: for every uncountable cardinal lam
bda\, every T-convexly valued (E\, O) has a unique-up-to-non-unique lamb
da-spherically complete el. extension which is weakly initial among the
lambda-spherically complete el. extensions and weakly terminal among the
"lambda-wim-constructible" extensions\, moreover such extension has the
same residue field as (E\,O) [1].\n\n[1] Freni\, P. (2024). T-convexity
\, Weakly Immediate Types and T-lambda-Spherical Completions of o-minima
l Structures. arXiv preprint arXiv:2404.07646.\n[2] Franz-Viktor Kuhlman
n\, Salma Kuhlmann\, and Saharon Shelah. Exponentiation in power series
fields. Proceedings of the American Mathematical Society\, 125(11):3177–
3183\, 1997\n[3] James Michael Tyne. T-levels and T-convexity. Universit
y of Illinois at Urbana-Champaign\, 2003\n[4] Lou Van Den Dries and Adam
H Lewenberg. T-convexity and tame extensions. The Journal of Symbolic L
ogic\, 60(1):74–102\, 1995.\n[5] Lou Van Den Dries and Patrick Speissegg
er. The field of reals with multisummable series and the exponential fun
ction. Proceedings of the London Mathematical Society\, 81(3):513–565\,
2000.\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1 (and zoom\, link in email)\, Alan Turing Building\
, Manchester
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