© Picture taken by Stephen Givant, Berkeley, June 1971

Set theory conference

A conference on the occasion of Ronald B. Jensen's 80th birthday

Institut für Mathematische Logik und Grundlagenforschung, WWU Münster

Aug 02--Aug 04, 2017

Organizers: Menachem Magidor (Jerusalem), Ralf Schindler (Münster), John Steel (Berkeley), W. Hugh Woodin (Harvard)

List of speakers:

We acknowledge generous support by the SFB 878 Groups, Geometry, and Actions.

Location: Lecture hall M4, Einsteinstrasse 62, Dept Math and CS, University of Münster.

Schedule:

Wed, Aug 02 Thu, Aug 03Fri, Aug 04
9:30--10:30

Gunter Fuchs

John Steel
11:00--12:00

Menachem Magidor

Adrian Mathias

Itay Neeman
14:30--15:30

Moti Gitik

Martin Zeman

W. Hugh Woodin
16:00--17:00

Bill Mitchell

Grigor Sargsyan
18:30--∞

Conference dinner

Talks and abstracts:

  1. Gunter Fuchs: Subcomplete forcing and its forcing principles

    Subcomplete forcing was introduced by Ronald Jensen. It is a class of forcings that don't add reals, are stationary set preserving, but may change cofinalities of regular cardinals to be countable. Jensen showed that Martin's axiom for subcomplete forcing is consistent, assuming the consistency of a supercompact cardinal, and that it is consistent with CH. This makes forcing principles for this class of forcings stand out. I will survey some results concerning such principles, which can be formulated for other classes of forcing as well, in terms of consistency strength calibrations and consequences. The principles include hierarchies of (weak) bounded forcing axioms, (virtual) resurrection axioms, and maximality principles. The weak/virtual principles arise from the original principles, formulated in terms of the existence of elementary embeddings, by requiring only the existence of generic embeddings, and it turns out that the consistency strengths of the arising principles can be determined precisely. The focus in terms of consequences of the principles is on the failure of (weak/threaded) square principles, but I will also mention principles that imply the existence of definable well-orderings of P(ω1). Time permitting, I will also talk about parametric generalizations of subcompleteness, which give rise to classes of forcings that enjoy nice closure properties and come with iteration theorems as well. Slides: Fuchs, Fuchs2.

  2. Moti Gitik: Extender based forcing with overlapping extenders and Shelah weak hypothesis

    Notes by rds: Gitik.

  3. Menachem Magidor: Inner models constructed by using generalized logics (ongoing work)

    I shall survey some recent developments in an ongoing project (jointly with J. Kennedy and J. Väänänen) in which we study inner models which are constructed similarly to L, but where we replace first order logic by some generalized logic. The issues we shall consider are basic properties and absoluteness of the models. Special role will be played by the model we get by using stationary logic. Slides: Magidor.

  4. Adrian Mathias: Linking descriptive set theory to symbolic dynamics

    In my paper "Analytic sets under attack", Mathematical Proceedings of the Cambridge philosophical Society, volume 138 (2005) pp 465-485, among other results concerning the iteration of the (backwards) shift function on Baire space, a recursive point was found for which the sequence of derived ω-limit sets does not stabilise until the first uncountable ordinal. This talk will present the main ideas in the hope that further development will follow, and will list some open problems. Slides: Mathias.

  5. Bill Mitchell: Sweating the Small Stuff

    Hamkins and Löwe asked whether it is consistent that VCol(ω , λ) ≡ V for every infinite cardinal λ. Mohamud Golshani and I showed that it is consistent, assuming large cardinal strength, and eventually exactly determined the necessary large cardinal strength: a sequence of extenders on a cardinal κ having a measure U together with κ+ many extenders having U as their associated normal ultrafilter. However, this statement is inprecise, it refers to the set of true sentences, and hence is not a sentence of ZFC. Here, we specify a mouse as the exact consistency strength of the Hamkins-Löwe property. Slides: Mitchell.

  6. Itay Neeman: Equiconsistencies at subcompact cardinals

    We present some equiconsistency results at the level of +n -subcompact cardinals for n< ω, assuming the strategic branches hypothesis for short extenders. For example we show assuming SBH that any threadable Woodin cardinal at which square fails is subcompact in an inner model. We discuss additional results at finite n>1, though these are less elegant since the exact characterization of square at these levels is still open. The results rely on the stacking methods that had been introduced by Jensen-Schindler-Schimmerling-Steel, adapted to long extender settings similar (and in retrospect equivalent) to ones developed by Woodin, with inner model constructions that are fully backgrounded by short extenders. This is joint work with John Steel. Slides: Neeman.

  7. Grigor Sargsyan: Recent results in descriptive inner model theory

    We will outline recent results in descriptive inner model theory, and will state open problems and research directions. Slides: Sargsyan.

  8. John R. Steel: What is a mouse?

    A mouse is an iterable premouse. Or is it? We shall discuss some of the varieties of premice, and the properties that iteration strategies can have. Then we shall suggest a definition of "mouse" in the short-extender realm that differs slightly from the "iterable premouse" formulation. Notes by rds: Steel.

  9. W. Hugh Woodin: The one generator framework

    We define the one generator framework for fine-structural strategic-extender models. Roughly, the one generator condition is simply the condition that extenders have a largest generator and at most one generator past the shortest initial segment not in their ultrapowers. This turns out to completely dictate essential features of the hierarchy with a number of surprising implications for the long-extender regime past the finite levels of supercompact. Notes by rds: Woodin.

  10. Martin Zeman: Constructing precipitous ideals with strong properties on small regular cardinals

    I will present a construction which produces precipitous ideals on small regular cardinals in a way that enables a lot of control of various parameters of the associated generic embeddings, like for instance the image of the critical point. The construction builds on the well-known Kunen-Magidor construction, but unlike the Kunen-Magidor construction, which needs an almost huge embedding to start with, it only uses an embedding at a superstrong level, which is much weaker and has significantly lower consistency strength. Notes by rds: Zeman.

If you wish to register for this conference and you are not a speaker and also not yet listed below as a "registered participant," you are kindly requested to send an email to Ralf Schindler at rds@wwu.de. Extended deadline for registration: July 21, 2017.

There is no registration fee, but we will ask participants for a small donation in order to cover expenses for coffee, tea, other drinks, and cookies.

There will be a conference dinner in the restaurant Il cucchiaio d'Argento on Aug 03, 2017. Registration for it closed. If you will participate and you are not in the set A+ = A ∪ partners of A, where A = speakers ∪ organizers ∪ { Ronald Jensen }, then you will have to pay for the dinner by yourself. There will be four choices of menues (meat, fish, vegetarian, vegan) for 30 € each. This does not include extra drinks.

Registered participants:

Juan P. Aguilera TU WienDinner: yes
Mariam Beriashvili Tbilisi Dinner: yes
Doug Blue Harvard Dinner: yes
Rupert McCallumTübingen Dinner: yes
Fabiana Castiblanco MünsterDinner: no
Justin Cavitt HarvardDinner: no
Vincenzo Dimonte UdineDinner: no
Henry Ehimetalor DenverDinner: no
Gabriel Fernandes MünsterDinner: yes
Gunter Fuchs CUNYDinner: yes
Moti Gitik Tel AvivDinner: yes
Gabriel Goldberg HarvardDinner: yes
Peter Göppert BochumDinner: no
Miha Habič CUNYDinner: no
Yair Hayut HU JerusalemDinner: no
Radek Honzik Charles University, PragueDinner: yes
Ronald Jensen HU BerlinDinner: yes 2x
Asaf Karagila Jerusalem Dinner: yes
Yurii Khomskii AmsterdamDinner: no
Martin Köberl RutgersDinner: yes
Jean LarsonUniversity of FloridaDinner: yes
Robert Lubarsky Boca RatonDinner: yes
Menachem Magidor HU JerusalemDinner: yes
Adrian Mathias ReunionDinner: yes 2x
Stefan Miedzianowski MünsterDinner: yes
Kaethe Minden CUNYDinner: no
Bill Mitchell GainesvilleDinner: yes 2x
Rahman Mohammadpour ParisDinner: yes
Itay Neeman UCLADinner: yes
Dan Saattrup Nielsen Bristol Dinner: no
William Parker Berlin Dinner: yes
Grigor Sargsyan RutgersDinner: yes 2x
Ralf Schindler MünsterDinner: yes 3x
Philipp Schlicht BonnDinner: yes
Farmer Schlutzenberg MünsterDinner: yes
John Steel UC BerkeleyDinner: yes 2x
Sarka Stejskalova Institute of Mathematics, PragueDinner: yes
Victor Torres-PerezViennaDinner: no
Sandra Uhlenbrock WienDinner: yes
Jouko Väänänen HelsinkiDinner: yes
Philip Welch BristolDinner: yes
Trevor Wilson Oxford, OHDinner: no
Hugh Woodin HarvardDinner: yes
Shi Xianghui BeijingDinner: yes
Martin Zeman UC IrvineDinner: yes
Yizheng Zhu MünsterDinner: yes


Housing information:

  • airbnb
  • Barbara's bed and breakfast, she has rooms for 25 -- 68 EUR. This is the only one not within walking distance, so you'd need a bike; but it's nice and cheap.
  • Nordstern hostel, rooms for 29 EUR.
  • My bed and breakfast, rooms for 49 -- 69 EUR.
  • Handwerkskammer Münster. They have very nice rooms for less than 100 € per week. Contact: Frau Iris Weverinck-Friedrichs, iris.weverinck@hwk-muenster.de, phone no. +49-251-705-1305.
  • Haus Niemann, rooms for 59,50 EUR.
  • Factory Hotel.
  • Hotel am Schlosspark.
  • Hotel Jellentrup.

    • Travel information:

    Münster has an airport, IATA code: FMO. You may e.g. fly there with Lufthansa (or, United, operated by Lufthansa 😊) via Frankfurt or Munich. A cab from FMO to the center is about 50 €, but there are shuttle buses for about 7 €. Another good option to reach Münster is to fly to Düsseldorf, IATA code: DUS, and take a train from there, which takes about 1 1/2 hours.

    Tourist information:

    The fifth Sculpture Projects Münster, see here, will take place in 2017: Skulptur Projekte.
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