Conference in Honor of Hugh Woodin's 60th Birthday
March 2729, 2015
Fong Auditorium (Boylston Hall)
Harvard University
Conference Schedule (PDF)
Friday, March 27, 2015.
2:003:00pm.
H. Garth Dales (University of Lancaster): Norming Infinitesimals of Large Fields. Abstract.
Long ago, I worked on a question of Kaplansky concerning the existence of discontinuous homomorphisms into a Banach algebra from the algebra $C(\Omega)$ of all continuous functions on a compact space $\Omega$. 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 hyperreal fields and superreal fields, that arise from algebras of continuous functions? Large cardinals come in here.
I claim that one particular field is a 'natural grownup version of the real line'. But it is open whether the infinitesimals of this field are normable. 
3:304:30pm.
Matthew D. Foreman (University of
California, Irvine): Strong Reflection Properties at $\omega_3$ and Huge
Cardinals. Abstract.
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.
 5:007:00pm. Reception at Harvard Faculty Club.
Saturday, March 28, 2015.
 9:0010:00am. Ronald Jensen (Humboldt University of Berlin): Subcomplete and Subproper Forcing.

10:3011:30am.
Alexander S. Kechris (California Insitute of
Technology): Descriptive Graph Combinatorics. Abstract.
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 wellbehaved in the topo logical or measure theoretic sense.  11:30am12:30pm.
Menachem Magidor (Hebrew University of Jerusalem): Inner
Models Defined from Generalized Logics and MM. Abstract
.
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 $\text{aa}$ logic (first order logic with the quantifier $\text{aa}P\Phi(P)$ 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). 
2:303:30pm.
Donald A. Martin (University of California, Los Angeles): Survey of Recent Work on Low Level Determinacy. Abstract.
By "low level," I mean Borel or low $\Delta^1_2$. 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.

4:005:00pm.
Grigor Sargsyan (Rutgers University): Forcing Axioms and the Solovay Hierarchy. Abstract.
We will show that PFA augmented by a mild large cardinal axiom implies that there is a model of $\text{AD}^+$ 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 determinacylike theories that are stronger than LSA. However, it is known that LSA is much weaker than a Woodin limit of Woodin cardinals.
Sunday, March 29, 2015.

9:0010:00am.
Theodore A. Slaman (University of California,
Berkeley): Woodin's Contributions to Recursion Theory. Abstract.
I will discuss Woodin’s contributions to Recursion Theory and the subsequent work that builds upon them.

10:3011:30am.
John R. Steel (University of California, Berkeley): Equiconsistencies at Subcompact Cardinals. Abstract.
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 $\delta \geq \omega_2$ 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.
The organizers ask that those planning to attend notify us at woodinbirthdayconference@gmail.com.
This meeting is supported by Harvard University and the National Science Foundation (partially through the MidAtlantic Mathematical Logic Seminar). Funding is available to support participant travel. Please write to the email address above to apply for support.
This meeting is supported by Harvard University and the National Science Foundation (partially through the MidAtlantic Mathematical Logic Seminar). Funding is available to support participant travel. Please write to the email address above to apply for support.
Hotels

Harvard Square Hotel.
Hotel Information.
110 Mt Auburn St
Cambridge
MA 02138
6178645200 
Sheraton Commander.
Hotel Information.
16 Garden Street
Cambridge
MA 02138
6175474800 
Gateway Inn.
Hotel Information.
211 Concord Turnpike
Cambridge
MA 02140
6176617800 
A Friendly Inn.
Hotel Information.
1673 Cambridge St
Cambridge
MA 02138
6175477851

The Irving House.
Hotel Information.
24 Irving St
Cambridge
MA 02138
6175474600 
Mary Prentiss Inn.
Hotel Information.
6 Prentiss St
Cambridge
MA 02138
6176612929 
Harding House.
Hotel Information.
288 Harvard Street
Cambridge
MA 02139
6178762888 
Parkside on Ellery.
Hotel Information.
74 Ellery Street
Cambridge
MA 02138
6174925025 
Whitman House.
Hotel Information.
17 Worcester Street
Cambridge
MA 02139
6179455350 
Kendall Hotel.
Hotel Information.
350 Main Street
Cambridge
MA 02142
8665661300 
Residence Inn.
Hotel Information.
6 Cambridge Center, 120 Broadway
Cambridge
MA 02142
6173490700 
Le Méridien CambridgeMIT.
Hotel Information.
20 Sidney Street
Cambridge
MA 02139
6175770200
Contact · Last updated: September 2014