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BEGIN:VEVENT
DTSTAMP:20240216T173904Z
DTSTART:20240221T151500Z
DTEND:20240221T163000Z
SUMMARY:Logic seminar: Pablo Andujar Guerrero (University of Leeds)
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}q2tx-lsk7tu
sl-8c98g8
DESCRIPTION:Title: Defining definable compactness\n\nAbstract: The first
notion of definable topological compactness was introduced within o-mini
mality in 1999 by K. Peterzil and C. Steinhorn for definable manifold sp
aces (e.g. definable groups)\, with the general motivation of extending
the role of compactness in topological algebra to the o-minimal setting.
Their definition was the property that every definable curve converges
(onwards curve-compactness). Its study was later motivated by the fact t
hat it played a crucial role in the formulation of Pillay's conjecture a
bout o-minimal definable groups. \n\nIn the 2000s the investigation of o
-minimal forking led to an equivalent characterization of definable comp
actness: every definable family of closed sets has a finite transversal.
The equivalence with a third notion\, that of having fsg (finitely sati
sfiable generics)\, was also observed. In the 2010s E. Hrushovski and F.
Loeser adapted curve-compactness to the valued field setting by conside
ring the property that every definable type converges. Furthermore\, aut
hors such as A. Fornasiero and W. Johnson started exploring yet another
notion of definable compactness: every definable filter of closed sets h
as non-empty intersection. The latter began extending the topological al
gebraic work of Peterzil and Steinhorn in o-minimality to the the field
of p-adics. In this talk we discuss the relationship between all the afo
rementioned definitions of definable compactness in various NIP settings
(including o-minimal\, p-adic and distal dp-minimal). We present the cu
rrent literature\, open questions\, and the model theory behind characte
rizing definable compactness.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1 (and zoom\, link in email)\, Alan Turing Building\
, Manchester
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