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


The contents of my cmu webpage which is not directly on this page can be found here


Invited Talks


Appalachian Set Theory

I was the scribe for two Appalachian Set Theory Workshops.

Itay Neeman's Workshop on Aronszajn Trees and the SCH. Notes

Moti Gitik's Workshop on Short Extender Forcing. Notes


Papers

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, submitted.

(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.


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.


Teaching

Forcing Summer School 2013

Math 223: Topics in Set Theory, Winter 2015

Math 114S: Introduction to Set Theory, Winter 2016

Graduate student logic seminar

Current schedule

History of the seminar