Very Informal European Gathering Bristol 2018










VIEG - 2018 

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



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:



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 or as usual AirBNB

Rodney Hotel to Howard House walking route


P D Welch's website



Martin Goldstern: “The Higher Cichon Diagram: lambda-andom reals’’



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


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


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

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.