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A HIERARCHY OF axiom SYSTEM ACG

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Science China Mathematics 1990年第2期33卷 129-134页

作者：张锦文 Institute of Software Academia Sinica

The study on the foundation of category was started in 1986, and the axiom system AGC has been developed for congolomerates. The consistency of the system ZF# and QM in the system ACG has been proved. A hierarchy of the systems: B0, B1,…,B. (n ∈ω),… is developed such that the consistency of any system within the sequence is provable in its succeeding systems, and the union of all systems in the sequence is just ACG, The consistency of the system ZF# and QM can be proved only in B0 although there exists a sequence of (?)0 axiom systems provided with increasing strength between system B and ACG.

关键词： hierarchy consistency axiom schema of predicative comprehension.

THE BOOLEAN-VALUED MODEL OF THE axiom SYSTEM OF GB

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Chinese Science Bulletin 1991年第2期36卷 99-102页

作者：李娜 Henan University Kaifeng 475001 PRC

Scott formulated his version of Boolean-valued models in 1967, He proved that the V（B） is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then, if B satisfies ccc and |B|=2No, V（B） GCH （see [1]）. In this note we construct the model △（B） on the basis of V（B）. Our main results are:（1）△（B）) is a Booleanvalued model of GB. （2） Assume the GCH. Then, if B satisfies ccc and |B|=2No, △（B） GCH. （3） The maximum and minimum principle is true in △（B）. （4） △（B）（B≠{0, 1}） is a Boolean-valued model of QM.

关键词： axiom system GB Boolean-valued model maximum and minimmn principle axiom system QM.

axiom Cosmology: A New Direction

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Journal of Modern Physics 2014年第18期5卷 2041-2048页

作者： Yonghong Liu School of Automation Wuhan University of Technology Wuhan China

In this work we have to deal with the axiomatization of cosmology, but it is only recently that we have hit upon a new mathematical approach to capitalize on our new set identities for the basic laws of cosmology. So our proposal of settlement is that we will propose some new laws (e.g., formation of the black hole). We introduce the concept of axiom cosmology. This principle describes the cosmology which can get freedom from the notion of the induction. We present a large-scale structure model of the universe, and this leads to successfully explanation of problem of closed universe or open universe (because from the outset it is theorem and its succinct proof). In this paper we prove that the non-singular point theorem means that a singularity cannot be mathematically defined nor physical. It allows us to overcome the mysterious, physical singularity conundrum and explain meaningful antimatter annihilations for general configurations.

关键词： axiom Cosmology Matter Antimatter Dark Matter Black Holes Singularity Large-Scale Structure

A Hierarchy of axiom Systems for Set Theory

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Chinese Quarterly Journal of Mathematics 1989年第3期4卷 7+1-6页

作者：张锦文中国科学院软件研究所

在文献[1,2]中,我们研究了范畴论基础,建立了集合的公理系统ACG,它能够处理超出了集合与类的极其大的汇合。本文进一步推广了系统ACG,建立了集合论公理系统的三个无穷序列:H0,H1,…;J0,J1,…,G0,G1,…。在建立这些公理系统的过程中,我... 详细信息

在文献[1,2]中,我们研究了范畴论基础,建立了集合的公理系统ACG,它能够处理超出了集合与类的极其大的汇合。本文进一步推广了系统ACG,建立了集合论公理系统的三个无穷序列:H0,H1,…;J0,J1,…,G0,G1,…。在建立这些公理系统的过程中,我们使用了类型论的方法,它们描述的能力是逐步增长的,

关键词：集合论公理系统 axiom 类型论范畴论无穷序列 Numbers 数学季刊 stored infinity proof

2002年Isuzu新型多功能越野车axiom

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汽车科技 2002年第2期 28-28页

作者：余景宏

FRAME MAPPINGS AND POINT SEPARATION axiomS OF TOPOLOGICAL SPACES

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数学年刊(英文版) 1988年第4期9卷 442-446页

作者：何明 The project is supported by the Science Fund of the Chinese Academy of Science.

In this paper, the author uses frame mappings to describe the T0 T1 and T2 axioms,and also gets a characterization of Sober space.

关键词： algebra 研云协万阳介无己初云 proof 才人加成 axiom

On an axiomatic Foundation for a Theory of Everything

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Journal of Philosophy Study 2021年第4期11卷 241-267页

作者： CUI Weicheng Key Laboratory of Coastal Environment and Resources of Zhejiang Province(KLaCER)School of Engineering Westlake UniversityHangzhouChina

Whether a unified theory of everything(TOE)is possible or not is a philosophical question and yes or no can be chosen in a two-valued logic *** the two schools are in conflict with each *** on the relativity of simultaneity axiom proposed in this paper,the present author suggests to use a midway philosophy to replace the present materialist philosophy for modern sciences;then this conflict together with many other conflicts among different theories such as classical mechanics(CM),general relativity(GR),and quantum mechanics(QM)can be solved and a unified theory of everything for the world we can observe can be *** this paper,the axiomatic foundation for a TOE is proposed which contains six fundamental *** problems related to these foundational issues are *** is hoped that the present paper might show a new promise and a new direction for TOE which would be helpful for the further development of modern sciences.

关键词： axiom mind-body problem the demarcation problem cause-effect law theory of everything(TOE)

Another proof for C^1 stability conjecture for flows

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Science China Mathematics 1998年第10期41卷 1076-1082页

作者：甘少波 Department of Mathematics Peking University Beijing China

The C 1 structural stability conjecture for flows by C 1 connecting lemma and obstruction sets is proved.

关键词： axiom A strong transversality obstruction set stability conjecture.

Inverse limits in the category of locales

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Science China Mathematics 1998年第5期41卷 476-482页

作者：贺伟刘应明 Department of Mathematics Shaanxi Teachers University Xi’an China Department of Mathematics Sichuan Union University Chengdu China

An explicit description of the construction of inverse limits of locales is given, and some properties of inverse limits of locales are shown by introducing a new type of limits\|collectionwise pullback. Specifically, a localic version of Steenrod theorem is proved without the axiom of choice and it is shown that an inverse limit of compact spatial loales is in general not spatial. As an application, the classic result by Steenrod is generalized.

关键词： category of locales inverse limit axiom of choice category of topological spaces.