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BEGIN:VEVENT
DTSTAMP:20191113T142751Z
DTSTART:20191120T150000Z
DTEND:20191120T160000Z
SUMMARY:Pantelis Eleftheriou - Expansions of o-minimal structures which i
ntroduce no new smooth functions
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}b8-k2xdpui9
-qtjieg
DESCRIPTION:Pantelis Eleftheriou joins us for the logic seminar.\n\n\n We
study expansions of o-minimal structures which preserve the tame geomet
ric behavior on the class of all definable sets. Two main categories ari
se according to whether there are dense-codense or infinite discrete def
inable sets. The expansion (R\, 2^Q) of the real field by all rational p
owers of 2 belongs to the first category. The expansion (R\, 2^Z) of the
real field by all integer powers of 2 belongs to the second category. I
n both cases we seek topological/analytical conditions that imply certai
n definable objects be R-definable. In the first structure\, it is known
that every open definable set is R-definable. In the second structure\,
we prove that every infinitely differentiable function with R-definable
domain is R-definable. We do this in a general axiomatic framework whic
h also allows R to be a reduct of a real closed field. This is joint wor
k with A. Savatovsky.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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