Will Boney

Research and Papers

Conferences and Talks


Mathematics Department
Harvard University
Cambridge, MA

Email: wboney@math.harvard.edu
Office: Science Center 238

I am a Benjamin Peirce Fellow and NSF Mathematical Sciences Postdoctoral Research Fellow, mentored by Hugh Woodin, at Harvard University.

I got my PhD under Rami Grossberg in 2014 at Carnegie Mellon University and spent a year working with John Baldwin at University of Illinois-Chicago before coming to Harvard.

I am organizing the logic seminar at Harvard. It meets Tuesdays at 5:15pm in Science Center 507.

I am currently teaching Math 255 Classification Theory for Tame Abstract Elementary Classes.

I'm interested in tame Abstract Elementary Classes. You can check out Wikipedia for more details, but the essence is that these are classes of structures in which types (appropriately defined as Galois types) satisfy a nice locality condition for equality. This locality condition can be seen as a weak form of compactness that is strong enough to recreated some classification theory, but weak enough to hold in many nonelementary classes.

My primary work and interest is around developing a classification theory for tame AECs. The "test question" here is Shelah's Categoricity Conjecture, but this is more of an organizing/motivating idea than the real goal. The goal is to develop notions of forking and independence that give us similar insight and dividing lines from first-order classification theory.

Beyond this, I'm also interested in model theory and classification theory in other nonelementary settings and concrete examples and applications of this classification theory to other areas of mathematics. Abutting these interests are first-order classification theory (and model theory) and the interaction between model theory and other areas of logic, especially set theory and category theory.

In 2014-2015, I gave several survey talks on tame AECs. An idealized version of the slides are available.

My CV is available (last updated 10/16).

I defended my dissertation in May 2014. Here is a collection of my papers and preprints. Click here for commentary and summaries. Please email me with any questions or comments
  1. Will Boney, Tameness from Large Cardinal Axioms, Journal of Symbolic Logic, vol 79, no 4, Dec 2014, 1092-1119. publisher version pdf arXiv

  2. Will Boney and Rami Grossberg, Forking in Short and Tame Abstract Elementary Classes, Annals of Pure and Applied Logic, vol 168, no 8, 2017, 1517-1551. publisher version pdf arXiv

  3. Will Boney, Tameness and Extending Frames, Journal of Mathematical Logic, vol 14, no 2, 2014. publisher version pdf arXiv

  4. Will Boney, Computing the Number of Types of Infinite Length, Notre Dame Journal of Formal Logic, vol 58, no 1, 2017, 133-154, publisher version pdf arXiv

  5. Will Boney, Rami Grossberg, Alexei Kolesnikov, and Sebastien Vasey. Canonical Forking in AECs, Annals of Pure and Applied Logic, vol 167, no 7, 2016, 590-613, publisher version, pdf arXiv

  6. Will Boney and Sebastien Vasey, Tameness and Frames Revisited, Accepted, Journal of Symbolic Logic, pdf arXiv, 36 pages (Updated 1/4/17).

  7. Will Boney, A Presentation Theorem for Continuous Logic and Metric Abstract Elementary Classes, Accepted, Mathematical Logic Quarterly, pdf arXiv, 27 pages (Updated 11/1/2016).

  8. Will Boney and Sebastien Vasey, Chain of Saturated Models in AECs, Archive for Mathematical Logic, vol 56, no 3, 2017, 187-213, publisher version pdf arXiv

  9. Will Boney and Sebastien Vasey, Categoricity and Infinitary Logics, Preprint, pdf arXiv, 9 pages (Updated 10/26/15).

  10. Will Boney and Monica VanDieren, Limit Models in Strictly Stable Abstract Elementary Classes, Submitted, pdf arXiv, 18 pages (Updated 2/23/16).

  11. Will Boney and Pedro Zambrano, Around the set-theoretical consistency of d-tameness of Metric Abstract Elementary Classes, Preprint, pdf arXiv, 9 pages (Updated 8/22/15).

  12. Will Boney and Spencer Unger, Large Cardinal Axioms from Tameness in AECs, Proceedings of the American Mathematical Society, vol. 145, no 10, 2017, 4517-4532, publisher version pdf arXiv.

  13. Will Boney, Rami Grossberg, Michael Lieberman, Jiri Rosicky and Sebastien Vasey. \mu-Abstract Elementary Classes and other generalizations, Jornal of Pure and Applied Algebra, vol 220, issue 9, Sep 2016, 3048-3066, publisher version pdf arXiv

  14. John Baldwin and Will Boney, Hanf Numbers and Presentation Theorems in AECs, Accepted, Beyond First Order Model Theory, pdf arXiv, 25 pages (Updated 7/25/16)

  15. Will Boney, The \Gamma-ultraproduct and averageable classes, Submitted, pdf arXiv, 26 pages (Updated 8/16/17)

  16. Will Boney, No Maximal Models from Looking Down, Preprint, pdf arXiv, 7 pages (Updated 11/2/15)

  17. Will Boney and Sebastien Vasey, A Survey on Tame Abstract Elementary Classes, Accepted, Beyond First Order Model Theory, pdf arXiv, 84 pages (Updated 7/22/16).

  18. Will Boney and Sebastien Vasey, Good Frames in the Hart-Shelah Example, Submitted, pdf arXiv, 31 pages (Updated 7/23/16).

  19. Will Boney, Definable Coherent Ultrapowers and Elementary Extensions, Submitted, pdf arXiv, 14 pages (Updated 8/20/17)

  20. Will Boney, Rami Grossberg, Monica VanDieren, and Sebastien Vasey, Superstability from Categoricity in Abstract Elementary Classes, Annals of Pure and Applied Logic, vol 168, no 7, 1383-1395, publisher version pdf arXiv

  21. Will Boney, Model Theoretic Characterizations of Large Cardinals, Preprint, pdf arXiv, 25 pages (Updated 8/24/17)
Here are a collection of informal reserach notes that I have written. Click here for commentary and summaries. Please email me with any questions or comments.
  1. Coheir in Averageable Classes, pdf

  2. Shelah's Omitting Types Theorem, pdf

  3. Feferman-Vaught Theorem, pdf

  4. Zilber's Pseudoexponentiation, pdf

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1402191.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

In Fall 2017, I am teaching Math 255 Classification Theory for Tame Abstract Elementary Classes.

I also teach Math 357 Topics in Model Theory for students interested in doing an advanced reading course in model theory. Contact me for more information.

I have previously taught Math 21a Multivariable Calculus, Math 21b Linear Algebra and Differential Equations, Math 144 Model Theory, and Math 145a Set Theory at Harvard. More information about my previous teaching is available here.

1. This photo was taken by Will Gunther on the top of the Sé de Évora in Évora, Portugal.
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