14 found
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Yong Cheng [10]Yongqiang Cheng [2]Yongtian Cheng [1]Yongmin Cheng [1]
Yongjin Cheng [1]
  1.  13
    Finding the Limit of Incompleteness I.Yong Cheng - 2020 - Bulletin of Symbolic Logic 26 (3-4):268-286.
    In this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem. We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ and $\textsf (...)
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  2.  21
    Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - forthcoming - Bulletin of Symbolic Logic:1-52.
  3.  25
    A New Dynamic Path Planning Approach for Unmanned Aerial Vehicles.Chenxi Huang, Yisha Lan, Yuchen Liu, Wen Zhou, Hongbin Pei, Longzhi Yang, Yongqiang Cheng, Yongtao Hao & Yonghong Peng - 2018 - Complexity 2018:1-17.
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  4.  31
    Large Cardinals Need Not Be Large in HOD.Yong Cheng, Sy-David Friedman & Joel David Hamkins - 2015 - Annals of Pure and Applied Logic 166 (11):1186-1198.
  5.  24
    Harrington’s Principle in Higher Order Arithmetic.Yong Cheng & Ralf Schindler - 2015 - Journal of Symbolic Logic 80 (2):477-489.
    LetZ2,Z3, andZ4denote 2nd, 3rd, and 4thorder arithmetic, respectively. We let Harrington’s Principle, HP, denote the statement that there is a realxsuch that everyx-admissible ordinal is a cardinal inL. The known proofs of Harrington’s theorem “$Det\left$implies 0♯exists” are done in two steps: first show that$Det\left$implies HP, and then show that HP implies 0♯exists. The first step is provable inZ2. In this paper we show thatZ2+ HP is equiconsistent with ZFC and thatZ3+ HP is equiconsistent with ZFC + there exists a remarkable (...)
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  6.  6
    On the Depth of Gödel’s Incompleteness Theorems.Yong Cheng - forthcoming - Philosophia Mathematica.
    ABSTRACT We use Gödel’s incompleteness theorems as a case study for investigating mathematical depth. We examine the philosophical question of what the depth of Gödel’s incompleteness theorems consists in. We focus on the methodological study of the depth of Gödel’s incompleteness theorems, and propose three criteria to account for the depth of the incompleteness theorems: influence, fruitfulness, and unity. Finally, we give some explanations for our account of the depth of Gödel’s incompleteness theorems.
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  7.  26
    Indestructibility Properties of Remarkable Cardinals.Yong Cheng & Victoria Gitman - 2015 - Archive for Mathematical Logic 54 (7-8):961-984.
    Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} is absolute for proper forcing :176–184, 2000). Here, we study the indestructibility properties of remarkable cardinals. We show that if κ is remarkable, then there is a forcing extension in which the remarkability of κ becomes indestructible by all <κ-closed ≤κ-distributive forcing and all two-step iterations of (...)
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  8.  23
    Forcing a Set Model of Z3 + Harrington's Principle.Yong Cheng - 2015 - Mathematical Logic Quarterly 61 (4-5):274-287.
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  9.  8
    Opinion Dynamics with the Contrarian Deterministic Effect and Human Mobility on Lattice.Long Guo, Yongjin Cheng & Zhongjie Luo - 2015 - Complexity 20 (5):43-49.
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  10.  28
    Effects of Badminton Expertise on Representational Momentum: A Combination of Cross-Sectional and Longitudinal Studies.Hua Jin, Pin Wang, Zhuo Fang, Xin Di, Zhuo’er Ye, Guiping Xu, Huiyan Lin, Yongmin Cheng, Yongjie Li, Yong Xu & Hengyi Rao - 2017 - Frontiers in Psychology 8.
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  11.  21
    Limited Usefulness of Capture Procedure and Capture Percentage for Evaluating Reproducibility in Psychological Science.Yongtian Cheng, Johnson Ching-Hong Li & Xiyao Liu - 2018 - Frontiers in Psychology 9.
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  12.  5
    Patient-Specific Coronary Artery 3D Printing Based on Intravascular Optical Coherence Tomography and Coronary Angiography.Chenxi Huang, Yisha Lan, Sirui Chen, Qing Liu, Xin Luo, Gaowei Xu, Wen Zhou, Fan Lin, Yonghong Peng, Eddie Y. K. Ng, Yongqiang Cheng, Nianyin Zeng, Guokai Zhang & Wenliang Che - 2019 - Complexity 2019:1-10.
    Despite the new ideas were inspired in medical treatment by the rapid advancement of three-dimensional printing technology, there is still rare research work reported on 3D printing of coronary arteries being documented in the literature. In this work, the application value of 3D printing technology in the treatment of cardiovascular diseases has been explored via comparison study between the 3D printed vascular solid model and the computer aided design model. In this paper, a new framework is proposed to achieve a (...)
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  13.  8
    The HOD Hypothesis and a Supercompact Cardinal.Yong Cheng - 2017 - Mathematical Logic Quarterly 63 (5):462-472.
    In this paper, we prove that: if κ is supercompact and the math formula Hypothesis holds, then there is a proper class of regular cardinals in math formula which are measurable in math formula. Woodin also proved this result independently [11]. As a corollary, we prove Woodin's Local Universality Theorem. This work shows that under the assumption of the math formula Hypothesis and supercompact cardinals, large cardinals in math formula are reflected to be large cardinals in math formula in a (...)
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  14.  9
    The Strong Reflecting Property and Harrington's Principle.Yong Cheng - 2015 - Mathematical Logic Quarterly 61 (4-5):329-340.
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