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DTSTART:20181028T020000
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
RDATE:20191027T020000
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DTSTART:20190329T020000
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UID:calendar.75629.field_date.0@mathematics.huji.ac.il
DTSTAMP:20200710T101547Z
CREATED:20190208T230015Z
DESCRIPTION:Date: \n\n2:00pm to 3:30pm\n\n\n\n\nSee also: Seminars\, Even
ts & Seminars\, Set TheoryLocation: \n\nRoss 63\n\n\nAbstract: In their 19
85 paper\, the above three authors introduced a consistent generalization
of Ramsey's theorem to pairs of countable ordinals\, which we abbreviate a
s $OCA_{ARS}$. This axiom asserts that for any continuous coloring (with r
espect to an appropriate topology) of pairs of countable ordinals\, there
is a decomposition of $\omega_1$ into countably-many homogeneous sets. The
key to their argument is to construct Preassignments of Colors. However\,
the known constructions of Preassignments only work over models satisfyin
g the CH\; this leads naturally to the question of whether $OCA_{ARS}$ is
consistent with a 'large continuum\,' i.e.\, with $2^{\aleph_0}>\aleph_2$.
Recently\, Itay Neeman and I have answered this question. The key to our
solution is to construct Preassignments with a substantial amount of 'symm
etry' and to combine them according to a specific recipe\, which we refer
to as Partition Product. In this talk\, we will motivate and define Partit
ion Products\, show how to construct symmetric preassignments\, and then s
how how we can use this machinery to obtain our result. \n\n Export\n \n
\n \nsubscribe iCal
DTSTART;TZID=Asia/Jerusalem:20190501T140000
DTEND;TZID=Asia/Jerusalem:20190501T153000
LAST-MODIFIED:20190427T190004Z
SUMMARY:Set Theory Seminar - Thomas Gilton (UCLA): Abraham-Rubin-Shelah Ope
n Coloring Axiom with a large continuum
URL;TYPE=URI:https://mathematics.huji.ac.il/event/set-theory-seminar-thomas
-gilton-ucla
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