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  1.  9
    $$I_0$$ I 0 and Combinatorics at $$\Lambda ^+$$ Λ +.Nam Trang & Xianghui Shi - 2017 - Archive for Mathematical Logic 56 (1-2):131-154.
    We investigate the compatibility of I0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_0$$\end{document} with various combinatorial principles at λ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda ^+$$\end{document}, which include the existence of λ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda ^+$$\end{document}-Aronszajn trees, square principles at λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, the existence of good scales at λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, stationary reflections (...)
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  2.  18
    Determinacy in L.Nam Trang - 2014 - Journal of Mathematical Logic 14 (1):1450006.
    Assume V = L ⊨ ZF + DC + Θ > ω2 + μ is a normal fine measure on.
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  3.  16
    Structure Theory of L and its Applications.Nam Trang - 2015 - Journal of Symbolic Logic 80 (1):29-55.
    In this paper, we explore the structure theory ofL under the hypothesisL ⊧ “AD +μis a normal fine measure on” and give some applications. First we show that “ ZFC + there existω2Woodin cardinals”1has the same consistency strength as “ AD +ω1is ℝ-supercompact”. During this process we show that ifL ⊧ AD then in factL ⊧ AD+. Next we prove important properties ofL including Σ1-reflection and the uniqueness ofμinL. Then we give the computation of full HOD inL. Finally, we use (...)
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  4.  8
    On a Class of Maximality Principles.Daisuke Ikegami & Nam Trang - 2018 - Archive for Mathematical Logic 57 (5-6):713-725.
    We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the principle MP\\) (...)
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  5.  2
    Tame Failures of the Unique Branch Hypothesis and Models of ADℝ + Θ is Regular.Grigor Sargsyan & Nam Trang - 2016 - Journal of Mathematical Logic 16 (2):1650007.
    In this paper, we show that the failure of the unique branch hypothesis for tame iteration trees implies that in some homogenous generic extension of [Formula: see text] there is a transitive model [Formula: see text] containing [Formula: see text] such that [Formula: see text] is regular. The results of this paper significantly extend earlier works from [Non-tame mice from tame failures of the unique branch bypothesis, Canadian J. Math. 66 903–923; Core models with more Woodin cardinals, J. Symbolic Logic (...)
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  6.  5
    Derived Models and Supercompact Measures on ℘Ω1).Nam Trang - 2015 - Mathematical Logic Quarterly 61 (1-2):56-65.