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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
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BEGIN:VEVENT
DTSTAMP:20220512T085622Z
DTSTART:20220525T140000Z
DTEND:20220525T150000Z
SUMMARY:Logic Seminar - Paul Shafer (Leeds)
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}w1kf-l27q71
c5-d93gqw
DESCRIPTION:Title: Cohesive powers of linear orders\n\nAbstract:\nA cohes
ive power of a computable structure is an effective analog of an ultrapo
wer\, where a cohesive set acts as an ultrafilter. We compare the prope
rties of cohesive powers to those of classical ultrapowers. In particul
ar\, we investigate what structures arise as the cohesive power of B ove
r C\, where B varies over the computable copies of some fixed computably
presentable structure A and C varies over the cohesive sets.\n\nLet ome
ga\, zeta\, and eta denote the respective order-types of (N\, <)\, (Z\,
<)\, and (Q\, <). We take omega as our computably presentable structure
\, and we consider the cohesive powers of its computable copies. If L i
s a computable copy of omega that is computably isomorphic to the standa
rd presentation (N\, <)\, then all of L's cohesive powers have order-typ
e omega + (zeta x eta)\, which is familiar as the order-type of countabl
e non-standard models of PA.\n\nWe show that it is possible to realize a
variety of order-types other than omega + (zeta x eta) as cohesive powe
rs of computable copies of omega. For example\, we show that there is a
computable copy L of omega whose power by any Delta_2 cohesive set has
order-type omega + eta. More generally\, we show that it is possible to
achieve order-types of the form omega + certain shuffle sums as cohesiv
e powers of computable linear orders of type omega.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1 (and zoom\, link in email)\, Alan Turing Building\
, Manchester
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