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TZID:Asia/Jerusalem
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DTSTART:20171029T020000
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
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DTSTART:20180323T020000
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UID:calendar.55193.field_date.0@mathematics.huji.ac.il
DTSTAMP:20191122T161637Z
CREATED:20180409T160349Z
DESCRIPTION:Date: \n\n11:00am to 1:00pm\n\n\n\n\nSee also: Logic\, Events
& Seminars\, SeminarsLocation: \n\nRoss 63\n\n\nAbstract: The set theoret
ic generalizations of algebras have been\nintroduced in the 1960s to give
a set theoretic interpretation of usual\nalgebraic structures. The shift i
n perspective from algebra to set\ntheory is that in set theory the focus
is on the collection of possible\nalgebras and sub-algebras on specific ca
rdinals rather than on\nparticular algebraic structures. The study of coll
ections of algebras\nand sub-algebras has generated many well-known proble
ms in combinatorial\nset theory (e.g.\, Chang’s conjecture and the existen
ce of small singular\nJonsson cardinals).\nIn the 1990s Foreman and Magido
r used algebras to initiate a study\nof Singular Stationarity\, i.e.\, a s
tudy of alternative notions of\nstationarity for subsets of singular cardi
nals. They introduced and\ndeveloped two notions of singular stationarity
called Mutual\nStationarity and Tight Stationarity\, and used their findin
gs to prove a\nfundamental result concerning generalized nonstationary ide
als.\nThe two notions of singular stationarity have been studied in the la
st\ntwo decades\, and the main purpose of the talk to describe the related
\nknown and recent results.\nI will start by giving some background materi
al on algebras and\nstationary sets\, and describe the history of a well-k
nown problem by\nJonsson. We will then proceed to describe the work done o
n the notion of\nMutually Stationary Sequences and sketch a recent proof w
hich is based\non the existence of special types of strong filters.\nIn th
e second part of the talk\, we will connect the notions of Singular\nStati
onarity to results from PCF theory and Extender-based forcing\nmethods.\n
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DTSTART;TZID=Asia/Jerusalem:20171227T110000
DTEND;TZID=Asia/Jerusalem:20171227T130000
LAST-MODIFIED:20191104T000111Z
SUMMARY:Logic Seminar - Omer Ben-Neria - 'Singular Stationarity and Set The
oretic Generalizations of Algebras'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/logic-seminar-omer-ben-ne
ria-singular-stationarity-and-set-theoretic-generalizations
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