Nam Trang

Mountain View
Visiting Assistant Professor
Department of Mathematics
University of Califorina, Irvine
Research Interest: Logic, Set Theory: fine structure, large cardinals, inner model theory, descriptive set theory, forcing axioms. My full research statement: pdf

Office: 410N Rowland Hall
Email address: ntrang[at]math[dot]uci[dot]edu

CV     Resume



1. HOD in Natural Models of AD^+ pdf, Annals of Pure and Applied Logic, 165(10):1533-1556, 2014.

2. Determinacy in L(R,\mu) pdf, Journal of Mathematical Logic, 14(01), 2014.

3. (with G.Sargsyan) Non-tame mice from tame failures of the unique branch hypothesis pdf, Canadian Journal of Mathematics, 66(4):903-923, 2014.

4. Derived models and supercompact measures on P_{\omega_1}(P(R)) pdf, Mathematical Logic Quarterly, 61(1-2):56-65, 2015.

5. Structure theory of L(R,\mu) and its applications pdf, Journal of Symbolic Logic, 80(01):29-55, 2015.

6. PFA and guessing models pdf, Israel Journal of Mathematics, 215 (2016), 607-667.

7. (with F. Schlutzenberg) Scales in hybrid mice over R pdf , submitted.

8. (with X. Shi) I_0 and combinatorics at lambda^+ pdf, Archive of Mathematical Logic, 56(1-2):131-154, 2017

9. Supercompactness can be equiconsistent with measurability pdf, submitted.

10. (with G.Sargsyan) Tame failures of the unique branch hypothesis and models of AD_R + Theta is regular pdf, Journal of Mathematical Logic, 16(02), 2016.

11. (with D. Rodriguez) L(R,\mu) is unique pdf, to appear on Advances in Mathematics.

12. (with F. Schlutzenberg) The fine structure of operator mice pdf, submitted.

13. (with D. Ikegami) On a class of maximality principles pdf, to appear on the Archive of Mathematical Logic.

14. (with T. Wilson) Determinacy from strong compactness of \omega_1 pdf, submitted.

15. (with J. R. Steel) Condensation for mouse pairs pdf, submitted.


1. (with G. Sargsyan) The Largest Suslin Axiom pdf, submitted.


1. 1st Irvine Conference on Descriptive Inner Model Theory and Hod Mice, 2016.


Generalized Solovay Measures, the HOD Analysis, and the Core Model Induction, pdf.

Warning: these notes may contain typos and errors.

(with J.R. Steel) AD^+ reflection pdf.

A Construction of a Coherent Sequence in K(R) pdf.

A Core Model Induction in L(S,R,mu) pdf.

A Hierarchy of Measures from AD_R pdf.

0-pistol hod mice from guessing hulls pdf.

(with T. Wilson) Supercompact measures on P_{\omega_1}(P(R)) pdf.


1. Generalized Solovay Measures, Aug. 2013, Math Colloquium, Miami University.

2. Structure Theory of L(R,\mu), Oct. 2013, AMS Meeting, Louisville.

3. Universality, Self-iterability, and Definability, Apr. 2014, MAMLS, Miami University.

4. On a Class of Guessing Models, May 2014, Young Set Theory workshop, Poland

5. The Core Model Induction and Guessing Models, June 2014, AIM and UC Berkeley workshops on DIMT

6. On a Class of Guessing Models, June 2014, BEST, UC Riverside

7. Hybrid Mice, Scales, and the Core Model Induction, Oct 2014, Rutgers Logic Conference

8. Uniqueness of L(R,mu), Jun 2015, BLAST, UNT, Denton, Texas

9. Squares in hod mice, Jul 2015, 3rd conference on descriptive inner model theory, Muenster, Germany

10. Large cardinals, determinacy, and forcing axioms, May 2016, ASL Annual Meeting, UConn.

11. Large cardinals, determinacy, and forcing axioms, Aug 2016, Logic Colloquium, Leeds.

12. Compactness of \omega_1, Set Theory workshop at UIC, Oct 2016.

13. Compactness of \omega_1, UCLA Logic Colloquium, Jan 2017, slides.

14. Forcing, elementary embeddings, and determinacy, JMM, San Diego, Jan 2018

15. Forcing and determinacy, Berkeley Logic Colloquium, UC Berkeley, Mar 23 2018