RTG Assistant Adjunct Professor

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

- In late October and Early November 2010, I gave a series of talks in the CMU logic seminar outlining some of my work on the tree property.
- On November 4 2011, I gave the CUNY Set Theory Seminar on the topic of branch lemmas and their application.
- On February 13 and 15 2012, I gave the University of California at Irvine Logic Seminar on the ineffable tree property.
- On September 24, 2013 I spoke at ESI in Vienna during the Forcing and Large Cardinals week of a six week Thematic Programme. Here are my slides.
- On October 8, 2013 I gave the University of Illinois Chicago logic seminar.
- On October 19, 2013 I spoke at the fall MAMLS meeting. Here are my slides.
- On February 7, 2014 I gave the UCLA Logic Colloquium on Successive cardinals with the tree property. The content of the talk is mostly contained in my slides from Irvine below.
- On March 3, 2014 I spoke in the UC Irvine logic seminar on Successive cardinals with the tree property. Here are my slides. Morally these should contain my result about the tree property up to aleph_{omega times 2}.
- On September 16, 2014 I spoke in the University of Illinois at Chicago Logic Seminar on successive cardinals with the tree property.
- On March 26, 2015 I spoke at the North America ASL meeting in the Set Theory special session.
- On March 30, 2015 I spoke at the Retrospective Workshop on Forcing and its Applications at the Fields institute.
- On April 17, 2015 I gave the UCLA logic seminar. I spoke about Tameness in abstract elementary classes and large cardinals.
- On June 17, 2015 I spoke at the 2015 Boise extravaganza of set theory at San Francisco State University. I spoke about Borel combinatorics and Baire measurable paradoxical decompositions.

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

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.

Gitik's Gap 2 short extender forcing

Gitik's Gap 2 short forcing with collapses

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

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.

Math 223: Topics in Set Theory, Winter 2015

Math 114S: Introduction to Set Theory, Winter 2016