2010 photo 


C. Ward Henson

Professor Emeritus
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street, Urbana, Illinois 61801-2975 USA.
email: henson(at)math(dot)uiuc(dot)edu


Slides for Henson's talk in the UIUC Logic Seminar on November 4, 2014, are linked here.  The title is Generic orbits and type isolation in the Gurarij space and the talk is a presentation of some of the content of a preprint with the same name, written jointly with Itai Ben Yaacov.  It has been known for awhile that in continuous model theory the Gurarij space is a Fraisse limit; it's theory is separably categorical and has quantifier elimination.  We have written clear and simple proofs of all those basic facts, and also have been studying the type spaces for this theory, over an arbitrary set of parameters, which we may as well take to be a separable Banach space E.  Our main achievement is to completely characterize isolated types in the type spaces over E, using tools from convex analysis.  This lets us derive a lot of information about the situation in which the set of isolated types is dense (for the logic topology) and hence there is an embedding T of E into the Gurarij space G such that the structure (G,T(e):e in E) is atomic; this is the same as saying there is a generic orbit in the Polish space of all such embeddings, under the action of Aut(G).  For example this happens for any E of dimension <= 3, for any finite dimensional E that is smooth or polyhedral, but not for all E -- we give an E of dimension 4 such that the isolated types over E are not dense, and we show that over many familiar infinite dimensional spaces E, there are no isolated types except for the obvious ones (coming from elements of E).  The tools from convex analysis that we develop should help answer several open questions about the Gurarij space, such as: how complex is the space of orbits of the action of Aut(G) on the unit sphere of G?  (We can derive a new result, that there are infinitely many orbits, but this is far from giving the final story.)

Slides for Henson's talk at the Midwest Model Theory Day on October 28, 2014, at UIC are linked here.  The title is Uncountably Categorical Banach Space Structures and the main new results have to do with examples of uncountably categorical Banach spaces that have been constructed/verified by Henson in joint work with Yves Raynaud, Univ. of Paris 6.  Similar talks were given earlier this year in Lyon, France, and at UCLA.  In the background is a weak form of the Baldwin-Lachlan theorems that has been proved for Banach structures by Shelah and Usvyatsov, in which Hilbert space plays a role analogous to that of a strongly minimal set.

Slides for Henson's talks in a mini course at the Hausdorff Institute for Mathematics, part of the University of Bonn, Germany, are linked here.  The talks were given Oct. 17, 21, and 23, 2013, for two hours each, under the general title Continuous first-order model theory for metric structures.  This mini course was offered in the framework of a program on Universality and Homogeneity organized at HIM during the Fall, 2013, by Alekos Kechris, Katrin Tent, and Anatoly Vershik.  (For complete information about this program, browse the information given here.)
The slides are here:  Lecture 1 (Oct 17); Lecture 2 (Oct 21); Lecture 3 (Oct 23).  (These are pdf files of beamer slides.)  Henson welcomes any comments or questions; they should be directed to him at the email address given above.



LOGIC AND MATHEMATICS 2011: this conference took place September 3-4, 2011, at UIUC.  Invited speakers were Itai Ben Yaacov (Lyon), Gregory Cherlin (Rutgers), Julien Melleray (Lyon), Anand Pillay (Leeds), Christian Rosendal (UIC), David Sherman (Virginia), and Henry Towsner (UCLA).  For more information, including the titles of talks and abstracts, look HERE.



Research Interests of CWH:
Articles on continuous first-order logic and the model theory of metric structures:


Recent teaching by CWH:



This page was last modified on November 4, 2014.