## Research and Papers | |

## Conferences and Talks | |

## Teaching | |

## Logic Seminar |

Mathematics Department

Harvard University

Cambridge, MA

Email: wboney@math.harvard.edu

Office: Science Center 238

I am a Benjamin Peirce Fellow 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. From 2014-2018, I was a NSF Mathematical Sciences Postdotoral Research Fellow, under Baldwin from 2014-2015 and under Hugh Woodin from 2015-2018.

I am co-organizing the logic seminar at Harvard with Sebastien Vasey. It meets Mondays at 5:40pm in Science Center 507.

In Spring 2019, I am teaching Math 141b Mathematical Logic II.

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.

In Fall 2017, I taught a graduate topics course on tame AECs. A rough version of the course notes are available here (and I hope to polish them soon). In Spring 2017, Sebastien Vasey taught a graduate topics course on AECs and his notes (mostly disjoint after introductory material) are available here.

My CV is available (last updated 9/18). My research and teaching statements are also available on request.

I defended my dissertation in May 2014.

- Will Boney,
*Advances in Classification Theory for Abstract Elementary Classes*, PhD Thesis, 2014, pdf, 162 pages.

- Will Boney,
*Tameness from Large Cardinal Axioms*, Journal of Symbolic Logic, vol 79, no 4, Dec 2014, 1092-1119. publisher version pdf arXiv

- 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

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

- 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

- 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

- Will Boney and Sebastien Vasey,
*Tameness and Frames Revisited*, Journal of Symbolic Logic, vol 82, no 3, 2017, 995--1021, publisher version, pdf arXiv.

- Will Boney,
*A Presentation Theorem for Continuous Logic and Metric Abstract Elementary Classes*, Mathematical Logic Quarterly, vol 63, no 5, 2017, 397--414, publisher version, pdf arXiv.

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

- 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.

- 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

- John Baldwin and Will Boney,
*Hanf Numbers and Presentation Theorems in AECs*, Beyond First Order Model Theory (José Iovino ed.), CRC Press (2017), 327–352. pdf arXiv

- Will Boney and Sebastien Vasey,
*A Survey on Tame Abstract Elementary Classes*, Beyond First Order Model Theory (José Iovino ed.), CRC Press (2017), 353–427. pdf arXiv

- Will Boney and Sebastien Vasey,
*Good Frames in the Hart-Shelah Example*, Archive for Mathematical Logic, vol 57, no 5-6, 687--712, publisher version, pdf arXiv.

- 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

- Will Boney and Sebastien Vasey,
*Structural Logic and Abstract Elementary Classes with Intersections*, Accepted, Bulletin of the Polish Academy of Sciences Mathematics, pdf arXiv, 14 pages (Updated 12/9/18).

- Will Boney,
*Model Theoretic Characterizations of Large Cardinals*, Accepted, Israel Journal of Mathematics, pdf arXiv, 31 pages (Updated 3/15/19)

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

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

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

- Nathanael Ackerman, Will Boney and Sebastien Vasey,
*Categoricity in Multiuniversal Classes*, Submitted, pdf arXiv, 16 pages (Updated 4/24/18).

- Will Boney and Ioannis Souldatos,
*A Lower Bound for the Hanf Number for Joint Embedding*, Submitted, pdf arXiv, 17 pages (Updated 8/9/18).

- Will Boney,
*Erdős-Rado Classes*, Submitted, pdf arXiv, 27 pages (Updated 10/22/18).

- Will Boney, Michael Lieberman,
*Tameness, Powerful Images, and Large Cardinals*, Submitted, pdf arXiv, 10 pages (Updated 4/3/19).

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

- 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).

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

- Coheir in Averageable Classes, pdf

- Shelah's Omitting Types Theorem, pdf

- Feferman-Vaught Theorem, pdf

- Zilber's Pseudoexponentiation, pdf

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 Spring 2019, I am teaching Math 141b Mathematical Logic II.

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 112 Real Analysis, Math 113 Analysis I: Complex Analysis, Math 144 Model Theory, and Math 145a Set Theory, and Math 255 Classification Theory for Tame Abstract Elementary Classes at Harvard. More information about my previous teaching is available here.