Nam D. Trang

Previous Scheduled Teaching

Published Intellectual Contributions

Journal Article

• Trang, N., Jackson, S.C., Chan, W. (2023). More definable combinatorics around the first and second uncountable cardinal. Journal of Mathematical Logic. 23 (03) World Scientific.
• Trang, N. (2023). The AD+ Conjecture and the Continuum Hypothesis. Proceedings of the American Mathematical Society. 151
• Trang, N., Jackson, S.C., Chan, W. (2021). The size of the class of countable sequences of ordinals. Transactions of the American Mathematical Society. https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2021-08573-6/
• Trang, N. (2021). Supercompactness can be equiconsistent with measurability. Notre Dame Journal of Formal Logic. 62 (4) 593-618. Duke University Press.
• Trang, N., Sargsyan, G. (2021). Sealing of the universally Baire sets. Bulletin of Symbolic Logic. 27 (3) 254-266. Cambridge University Press.
• Trang, N., Wilson, T. (2021). Determinacy from Strong Compactness of \omega_1. Annals of Pure and Applied Logic. 172 (6) Elsevier.
• Trang, N., Sargsyan, G. (2021). Sealing from iterability. Transactions of the American Mathematical Society. 229-248. https://www.ams.org/journals/btran/2021-08-07/S2330-0000-2021-00065-5/
• Trang, N., Ikegami, D. (2020). On supercompactness of $\omega_1$. Springer.
• Trang, N., Rodriguez, D. (2018). L(R,\mu) is unique. Advances in Mathematics. 324 355--393. Elsevier.
• Trang, N., Ikegami, D. (2018). On a class of maximality principles. Archive for Mathematical Logic. 57 (5-6) 713--725. Springer.
• Trang, N., Shi, X. (2017). I_0 and combinatorics at lambda^+. Archive for Mathematical Logic. 56 (1-2) 131--154. Springer.
• Trang, N. (2016). PFA and guessing models. Israel Journal of Mathematics. 216 607-667.
• Trang, N., Sargsyan, G. (2016). Tame failures of the unique branch hypothesis and models of AD_R + Theta is regular. Journal of Mathematical Logic. 16 (02) 28. World Scientific.
• Trang, N. (2015). Derived models and supercompact measures on P_{\omega_1}(P(R)). Mathematical Logic Quarterly. 61 (1-2) 56--65. Elsevier.
• Trang, N. (2015). Structure theory of L(R,\mu) and its applications. The Journal of Symbolic Logic. 80 (01) 29--55.
• Trang, N. (2014). Determinacy in L(R,\mu). Journal of Mathematical Logic. 14 (01) World Scientific.
• Trang, N., Sargsyan, G. (2014). Non-tame mice from tame failures of the unique branch hypothesis. Canadian Journal of Mathematics. 66 (4) 903--923.
• Trang, N.D. (2014). HOD in Natural Models of $\sf{AD}^+$. Annals of Pure and Applied Logic. 165 (10) 1533-1556. Elsevier.

Survey paper

• Trang, N. (2020). A brief account of recent developments in inner model theory. This is part of the volume on Simon Thomas' birthday. 752 American Mathematical Society.

Contracts, Grants and Sponsored Research

Grant - Research

• Trang, N.D. (Co-Principal), "AIM SQUARE : Large cardinal axioms and left-distributive algebras," sponsored by AIM (the American Institute of Mathematics), International, Funded. (2023 - 2025).
• Trang, N.D., "CAREER: CURRENT AND FUTURE DEVELOPMENTS OF THE CORE MODEL INDUCTION," sponsored by National Science Foundation, Federal, $403716 Funded. (2020 - 2025).
• Trang, N.D. (Principal), "Descriptive Inner Model Theory and its Applications," sponsored by National Science Foundation, Federal, $120591 Funded. (2019 - 2022).
• Trang, N., "UNT Junior Research Grant," sponsored by UNT, University of North Texas, $5000 Funded. (2020 - 2020).
• Trang, N., "UNT Junior Faculty Research Grant," sponsored by University of North Texas, University of North Texas, $5000 Funded. (2019 - 2019).
• Trang, N. (Principal), "NSF grant," sponsored by The National Science Foundation, Federal, $95359 Funded. (2016 - 2019).
• Trang, N.D. (Principal), "CAREER: Current and Future Developments of the Core Model Induction," sponsored by National Science Foundation, FED, Funded. (2020 - 2025).
• Trang, N.D. (Principal), "Descriptive Inner Model Theory, Large Cardinals, and Combinatorics," sponsored by National Science Foundation, FED, Funded. (2018 - 2020).
• Trang, N.D. (Principal), "Descriptive Inner Model Theory and Its Applications," sponsored by National Science Foundation, FED, Funded. (2019 - 2020).
• Trang, N. (Principal), "NSF grant," sponsored by The National Science Foundation, Federal, Funded. (2016 - 2019).