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In black: Fong Auditorium
(Boylston), the Faculty Club,
and the Society of Fellows
(Eliot House)
Conference in Honor of
Hugh Woodin’s 60th Birthday
Friday, March 27:
2:00 - 3:00
Fong Auditorium
(Boylston Hall 110)
11:30 - 12:30
Norming Infinitesimals of Large Fields
Fong Auditorium
3:30 - 4:30
Strong Reflection Properties at ω3
and Inner Models with Huge Cardinals
The subjects that will be discussed in the talk are part of an ongoing project (jointly with
J. Kennedy and J. Vaananen) of studying the inner models one gets by imitating the construction of the constructible universe L, but replacing “first order definability” in the
successor stage of the construction by “definable by the logic L” where L is a logic generalizing first order logic.
In the talk we shall concentrate on the model constructed using the “aa” logic (first
order logic with the quantifier aaP Φ(P) meaning “for a club of countable subsets of the
model Φ(P) holds.” We shall be especially interested in the inner model one gets by using
this logic in a universe of Set Theory satisfying Martin’s Maximum (MM).
2:30 - 3:30
Survey of Recent Work on Low Level Determinacy
4:00 - 5:00
Reception
(Library)
Saturday, March 28:
8:15 - 9:00
Ticknor Lounge
(Boylston Hall)
9:00 - 10:00
Fong Auditorium
(Boylston Hall 110)
10:30 - 11:30
Subcomplete and Subproper Forcing
Ronald Jensen
Descriptive Graph Combinatorics
Alexander S. Kechris
This talk is about a relatively new subject, developed in the last two decades or so, which
is at the interface of descriptive set theory and graph theory but also has interesting connections with other areas such as ergodic theory and probability theory.
The object of study is the theory of definable graphs, usually Borel or analytic, on
Polish spaces and one investigates how combinatorial concepts, such as colorings and
matchings, behave under definability constraints, i.e., when they are required to be definable or perhaps well-behaved in the topological or measure theoretic sense.
Grigor Sarsysan
Sunday, March 29:
8:15 - 9:00
Breakfast
Forcing Axioms and the Solovay Hierarchy
We will show that PFA augmented by a mild large cardinal axiom implies that there is
a model of AD+ in which there is a Largest Suslin cardinal which is a member of the
Solovay sequence. The aforementioned determinacy theory, known as LSA, is one of the
strongest pure determinacy theories known to us. We will also have a discussion of determinacy-like theories that are stronger than LSA. However, it is known that LSA is much
weaker than a Woodin limit of Woodin cardinals.
A consistent variant of Chang’s Conjecture is presented that implies an inner model with a
huge cardinal. The proof is quite elementary and will be presented.
Harvard Faculty Club
Donald A. Martin
By “low level,” I mean Borel or low ∆12. I will discuss recent results on the exact of strength
of determinacy for various low level pointclasses, and I will mention some questions that
remain open.
Matthew Foreman
5:00 - 7:00
Menachem Magidor
(Boylston Hall 110)
H. G. Dales
Long ago, I worked on a question of Kaplansky concerning the existence of discontinuous
homomorphisms into a Banach algebra from the algebra C(Ω) of all continuous functions on a compact space Ω. I shall recall this problem and some reformulations, and note
that with CH, such discontinuous homomorphisms were constructed by myself and by
Jean Esterle. I shall also explain that Hugh Woodin proved that there are models of ZFC
in which all such homomorphisms are continuous. Thus the question is independent of
ZFC.
One reformulation involves norming the infinitesimals of a large ordered field. This
leads to two natural questions. First, for which fields is this possible? Second, when are
ordered fields isomorphic to fields, such as hyper-real fields and super-real fields, that
arise from algebras of continuous functions? Large cardinals come in here.
I claim that one particular field is a ‘natural grown-up version of the real line’. But it is
open whether the infinitesimals of this field are normable.
Inner Models Defined from Generalized Logics and MM
Ticknor Lounge
(Boylston Hall)
9:00 - 10:00
Fong Auditorium
Breakfast
Woodin’s Contributions to Recursion Theory
Theodore A. Slaman
(Boylston Hall 110)
I will discuss Woodin’s contributions to Recursion Theory and the subsequent work that
builds upon them.
10:30 - 11:30
Equiconsistencies at Subcompact Cardinals
John Steel
We say that a regular cardinal delta is threadable just in case every coherent sequence of
clubs of length delta can be properly extended. It is consistent relative to supercompact
cardinals that every δ ≥ ω2 is threadable. It seems likely that the converse relative consistency statement is true. We describe some work in this direction due to Itay Neeman
and the author.
Organizers: Peter Koellner (919) 698-2532, Paul Larson (301) 580-8412, Gabriel Goldberg (323) 206-1749