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VIEG - 2018
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The VIEG - 2018
will be held on Fri.-Sat. June 8-9th , 2018 at the School of
Mathematics, University of Bristol
Speakers and the intended time of their lectures:
- David Asperó (UEA) Friday 16.45 - 17.45
- Adrian Mathias (Reunion) Saturday 11.30 - 12.30
- Mirna Džamonja (UEA) Friday 14.00 - 15.00
- Martin Goldstern (TU Vienna) Saturday 10.30 -11.30
- Asaf Karagila (UEA) Friday 15.30 - 16.30
- Benedikt Löwe (Hamburg, ILLC Amsterdam) Saturday 9.00 - 10.00
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The Workshop will
take place in 4th Floor Seminar Room of Howard House, School of Mathematics,
University of Bristol, Queen’s Avenue, BS8 1SD (commencing at lunch time on the Friday, and
finishing early Saturday afternoon).
See Heilbronn Institute on the map: http://www.bristol.ac.uk/maps/google/
Travel: The
Bus/Coach station is within a fairly stiff 10/15 min. walk of Howard House
and Berkeley Square. From Heathrow the express coach is direct and is almost the
easiest way to get to Bristol. In Bristol, bus numbers 8, 9 from the train
station (or from near the Bus Station) will take you very near the Berkeley
Square Hotel; (“Parkstreet Top”) they also stop at “The Triangle West” (close to Howard
House). Bus Number 8 goes on to the Rodney Hotel (“by the Quadrant pub'', in Clifton).
If you do use the
train be sure to buy your tickets in advance, as otherwise these can be
ruinously expensive.
For Accommodation:
The Rodney Hotel (in Clifton) and
The Berkeley Square Hotel will house most speakers. Postgrads may wish to consider Toad Lodge http://www.toadlodge.uk.com
or as usual AirBNB
Rodney Hotel to Howard House walking route
P D Welch's website
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Martin
Goldstern: “The
Higher Cichon Diagram: lambda-andom
reals’’
Slides
In a joint paper with Thomas Baumhauer and Saharon Shelah, we investigate
the cardinal characteristics introduced by Shelah
in his paper
"A parallel to the null ideal for inaccessible lambda, part
I" [Sh:1004]
and their connection to the characteristics of other ideals, in particular
the meager ideal and the ideal of nowhere
stationary sets. I will
present ZFC results and independence results from this paper.
Adrian
Mathias: “A proof of Eugene Wesley revisited’’
The paper {\it Extensions of the measurable choice theorem by means of forcing} by Eugene Wesley, a doctoral student of
Robert Aumann, was published in the Israel Journal of Mathematics in Volume 14, 1973, pp 104-14.
His proofs use Solovay's random-real forcing over models of ZFC to extend results of von Neumann. On page 113 he asks whether models of
Zermelo set theory will suffice for his proofs. My answer is ``No, but nearly."
Z alone cannot support the usual definitions of forcing, as shown in [Brussels]. But the theory Z + PROVI + DC, which is equiconsistent
with Z, is sufficient for Wesley's arguments provided both Mostowski's absoluteness argument for $\LP11$ predicates and
the coding of Borel sets in Solovay's famous paper [S] are appropriately modified.
Asaf Karagila:
Critical failures
We will define the notion of a critical cardinal in ZF, discuss a lifting
criterion that allows us to obtain some results about critical cardinals, and
outline some success and some failures related to this work. This is a joint
project with Yair Hayut.
Mirna Džamonja:
Higher order versions of the logic of chains
Slides
First order logic of chains was discovered by Carol Karp
and revisited in recent work of Dz. with Jouko Vaananen. The results have shown that the logic, defined
through a singular cardinal of countable cofinality,
behaves very much like the first order logic. In our new joint work, we study
higher order versions of the logic of chains and their fragments to defend
the thesis that in this context we can also recover similarities with the
ordinary logic.
David Asperó:
Side conditions, adding few reals, and trees
Slides
I will present a method for building forcing iterations with small support and at the same time preserving (some initial segment of) GCH. The focus will be on a recent application to trees on omega_2.
Benedikt Löwe:
Order types of models of fragments and reducts of PA
Slides
We shall consider the following six theories: Peano Arithmetic with and without induction (PA and PA-), Presburger Arithmetic with and without induction (Pr and Pr-), and Successor Arithmetic with and without induction (SA and SA-). Order types of models of PA and Pr have been studied by Bovykin, Kaye, Potthoff, and Zoethout. For any pair (S,T) from our six theories such that S does not prove T, we shall give examples of order types that separate S from T, i.e., an order type of a model of S that cannot be an order type of a model of T. This is joint work with Lorenzo Galeotti.
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