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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20240510T141630Z
DTSTART:20240515T141500Z
DTEND:20240515T153000Z
SUMMARY:Logic seminar: Ricardo Palomino
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}o6k-lvmjli3
2-uwjj4n
DESCRIPTION:Title: Local real closed SV-rings of finite rank and their mo
del theory\n\nAbstract: A commutative and unital ring A is a survaluatio
n ring\, or SV-ring for short\, if A/ is a valuation ring for all prime
ideals of A. SV-rings were first introduced in the early 1990s within t
he context of rings of continuous functions\, and since then\, they have
mostly gained the attention of the mathematical community which works o
n lattice-ordered groups and rings. The class of all SV-rings turns out
to not be elementary in the language of rings\, but some subclasses are\
; in particular\, the class of local real closed SV-rings of rank at mos
t m ? ? is elementary\, and this talk will be focused on the algebra and
model theory of SV-rings in this latter class. It turns out that a rin
g is a local real closed SV-ring of rank at most m ? ? if and only if i
t is isomorphic to a finite iterated fibre product of at most m non-triv
ial real closed valuation rings (i.e.\, proper convex subrings of real c
losed fields) along surjective ring homomorphisms\; I will sketch the pr
oof of this structure theorem\, and then use it\, together with some con
structions involving those valuation rings corresponding to the canonica
l valuation on real closed Hahn fields\, to show that much of the good m
odel theory of real closed valuation rings is preserved to various eleme
ntary subclasses of local real closed SV-rings of finite rank.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1 (and zoom\, link in email)\, Alan Turing Building\
, Manchester
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