Date: August 13th (Mon.)
Place: P-017 (The Euclides building )
Time schedule:
10:00-10:30 Coffee and cookies
10:30-11.30 Peter Koepke,
"Sets in Prikry Extensions"
11:30-13:00 Lunch
13:00-14:00 Joel
David Hamkins , "There is no nontrivial elementary embedding from one
ground model to another"
14:00-14:15 Break
14:15-15:15 Luca Motto Ros ,
"A dichotomy theorem for Borel reducibilities"
15:15-15:30 Break
15:30-16:30 Brian Semmes ,
"Jayne-Rogers with Games"
16:30-16:45 Break
16:45-17:45 Ali Enayat,
"In praise of nonstandard models"
Abstracts:
1. Peter
Koepke
Title "Sets in Prikry Extensions"
Abstract. Prikry forcing turns a measurable cardinal
$\kappa$ into a singular cardinal by generically adjoining an $\omega$-sequence
$C=\{c_0,c_1,\dots\}$ cofinal
in $\kappa$.
We show that every subset $x\subseteq\kappa$ in the Prikry extension $V[C]$ of the
ground model $V$ is {\it equiconstructible} with some
$D\subseteq C$ over $V$, i.e., $x$ is constructible
from parameters in $V\cup\{D\}$ and $D$ is constructible from parameters in
$V\cup\{x\}$. This supports the open conjecture that every intermediate
transitive model $N$, $V \subseteq N \subseteq V[C]$ is of the form
$N=V[D]$ for some $D \subseteq C$. (joint work with Vladimir Kanovei,
2. Joel
David Hamkins
Title "There is no nontrivial elementary embedding from one ground model
to another"
Abstract. Kunen's famous inconsistency theorem shows
that there is no nontrivial elementary embedding j:V to V. This was extended by Woodin
to show that there is no nontrivial elementary embedding from any forcing
extension V[G] to V. (Another way to say the same
thing is that if j:V to M, then V is not a forcing
extension of M.) I will speak on generalizations ruling out j:V to V[G], and also j:M to
N, whenever M and N are ground models of a common forcing extension, in which j
is a class. Time permitting, I will also show there is no j:V to HOD and no j:HOD to
V.
3. Luca
Motto Ros
Title "A dichotomy theorem for Borel reducibilities"
Abstract. We will survey some recent developments in the theory of the general reducibilities for sets of reals,
and present a dichotomy theorem which essentially says that almost every Borel set of reductions induce a degree-structure which is
isomorphic either to the Lipschitz or to the Wadge one.
4. Brian
Semmes
Title "Jayne-Rogers with Games"
Abstract. In this talk I will sketch a game-theoretic proof of the Jayne-Rogers
theorem.
5. Ali
Enayat
Title "In praise of nonstandard models"
Abstract. For many set theorists, nonstandard models of ZF are pathological and
devoid of serious mathematical interest. To correct this view, I will present a
variety of old and new results to convey the beauty and mystery of nonstandard
models.
6. Philip Welch
TBA
Direction: To get to the Euclides
building, please refer to this
website.
If you have any question, please contact Daisuke
Ikegami