Spencer Unger

RTG Assistant Adjunct Professor

Department of Mathematics

University of California Los Angeles

My office is MS 7336

I can be reached via email at: sunger at math (dot) ucla (another dot) edu

Research interests

My research is in set theory and mathematical logic. I am interested in questions in combinatorial set theory using forcing and large cardinals, the model theory of abstract elementary classes and descriptive set theory.


Papers are listed in roughly chronological order

Fragility and indestructibility of the tree property, Archive for Mathematical Logic 51 (2012) 635-645. Here is the link to the Springer page with this article.

Aronszajn Trees and the successors of a singular cardinal, Archive for Mathematical Logic 52 (2013) 483-496. Here is the link to the Springer page.

(Joint with Dima Sinapova) Combinatorics at aleph_omega, Annals of Pure and Applied Logic 165 (2014) 996-1007. Also at Science Direct.

A model of Cummings and Foreman revisited, Annals of Pure and Applied Logic 165 (2014) 1813-1831. Also at Science Direct

Fragility and indestructibility II, Annals of Pure and Applied Logic 166 (2015) 1110-1122.

(Joint with Dima Sinapova) Scales at aleph_omega, Israel Journal of Math, 209 (2015) 463-486.

The tree property below aleph_{omega times 2}, Annals of Pure and Applied Logic, 167 (2016) 247-261.

Iterating along a Prikry sequence, Fundamenta Mathematicae, 232 (2016).

(Joint with Andrew Marks) Borel measurable paradoxical decompositions via matchings, Advances in Mathematics, 289 (2016) 397-410.

(Joint with Dima Sinapova) Modified extender based forcing, submitted.

(Joint with Will Boney) Large cardinal axioms from tameness in AECs, accepted for publication in The Proceedings of the AMS.

(Joint with Dima Sinapova) The tree property at aleph_{omega^2+1} and aleph_{omega^2+2}, submitted.

(Joint with Yair Hayut) The strong tree property and weak square, submitted.

(Joint with Omer Ben-Neria and Chris Lambie-Hanson) Diagonal supercompact Radin forcing, submitted.

(Joint with Omer Ben-Neria) Homogeneous changes in cofinalities with applications to HOD, submitted.

(Joint with Andrew Marks) Borel circle squaring.

Successive failures of approachability, submitted.

Research notes:

Gitik's Gap 2 short extender forcing

Gitik's Gap 2 short forcing with collapses

Solovay's model

Compactness for the chromatic number at aleph_{omega_1 +1}

Other mathematical writing

Lecture notes for seminars given at CMU aimed at a general graduate student audience on the subjects of forcing, large cardinals and trees.

Four talks given at CMU on Mitchell's forcing to get the tree property at $\aleph_2$. Talk 1, Talk 2, Talk 3, Talk 4.

Three talks given at CMU on PCF theory Talk 1, Talk 2, Talk 3.


Since the fall of 2013, I have been teaching various undergraduate courses at UCLA including quite a few large lecture courses. Information about these courses can be found on their respective CCLE pages. The links below are for the purely logic/set theory courses that I have taught.

Forcing Summer School 2013

Math 223: Topics in Set Theory, Winter 2015

Math 114S: Introduction to Set Theory, Winter 2016

Graduate student logic seminar

Below are the pages for the logic seminar that I have been running at UCLA since the fall of 2013.

Current schedule

History of the seminar