Nam Trang

Mountain View
Assistant Professor
Department of Mathematics
University of North Texas, Denton
Research Interest: Logic, Set Theory: fine structure, large cardinals, inner model theory, descriptive set theory, forcing axioms.
Office: 418B General Academic Building
Email address: Nam[dot]Trang[at]math[dot]unt[dot]edu


My brief research statement: pdf     My full research statement: pdf


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, Notre Dame Journal of Formal Logic, 62(4): 593-618, 2021.

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, Advances in Mathematics, 324(14), 2018.

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

13. (with D. Ikegami) On a class of maximality principles pdf, Archive of Mathematical Logic, 57(5-6):713-725, 2018.

14. (with T. Wilson) Determinacy from strong compactness of \omega_1 pdf, Annals of Pure and Applied Logic, 176 (6), 2021.

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

16. (with D. Ikegami) On supercompactness of \omega_1 pdf, Takeuti's volume, 2020.

17. (with G. Sargsyan) Sealing from iterability pdf, Transactions of the AMS Series B, 8: 229-248, 2021.

18. (with G. Sargsyan) The exact consistency strength of generic absoluteness for universally Baire sets pdf, submitted.

19. (with W. Chan and S. Jackson) More definable combinatorics around the first and second uncountable cardinal pdf, to appear on the Journal of Mathematical Logic.

20. Divergent models with the failure of the continuum hypothesis pdf, submitted.

21. (with W. Chan and S. Jackson) The size of the class of countable sequences of ordinals pdf, Transactions of the AMS, 375: 1725-1743, 2022.

22. (with W. Chan and S. Jackson) Countable length everywhere club uniformization pdf, to appear on the Journal of Symbolic Logic.

23. The AD+ Conjecture and the Continuum Hypothesis pdf , to appear on the Proceedings of the AMS.

24. (with D. Adolf, G. Sargsyan, T. Wilson, M. Zeman) Ideals and Strong Axioms of Determinacy pdf, submitted.

25. (with W. Chan and S. Jackson) Almost everywhere behavior of functions according to partition measures pdf,submitted.

26. (with W. Chan and S. Jackson) Almost disjoint families under determinacy pdf, submitted.

27. (with S. Jackson, C. Olsen, J. Sweatt, A. Yuan) On the cop number of subdivisions of graphs pdf, submitted.


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


1. A brief account of recent developments in inner model theory pdf, Simon Thomas volume, 2020.

2. (with G. Sargsyan) Sealing of the universally Baire sets pdf, to appear on the Bulletin of Symbolic Logic.


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

16. Tutorial on the Core Model Induction, Rutgers Set Theory summer schoo, June 2019

17. The consistency strength of Sealing, XVI International Set Theory Workshop, Luminy, France, Sep 23-27, 2019