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James H. Schmerl 《Mathematical Logic Quarterly》2000,46(4):543-548
Improving a theorem of Gasarch and Hirst, we prove that if 2 ≤ k ≤ m < ω, then the following is equivalent to WKL0 over RCA0 Every locally k‐colorable graph is m‐colorable. 相似文献
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Jeffry L. Hirst 《Mathematical Logic Quarterly》1998,44(4):459-464
This paper uses the framework of reverse mathematics to analyze the proof theoretic content of several statements concerning multiplication of countable well-orderings. In particular, a division algorithm for ordinal arithmetic is shown to be equivalent to the subsystem ATR 0. 相似文献
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《Annals of Pure and Applied Logic》2022,173(8):103133
In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a number of natural variants of these theorems are equivalent, or closely related, to the “big five” subsystems of reverse mathematics.The results of this paper explore the relationship between graph theory and logic by showing the way in which specific changes to a single graph-theoretic principle impact the corresponding proof-theoretic strength. Taken together, the results and questions of this paper suggest that the existence of matchings in countable graphs provides a rich context for understanding reverse mathematics more broadly. 相似文献
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Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to formulas without parameters. Based on this axiom, we formulate a base theory for the Reverse Mathematics of Nonstandard Analysis and prove some natural reversals, and show that most of these equivalences do not hold in the absence of parameter-free Transfer. 相似文献
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Jeffry L. Hirst 《Mathematical Logic Quarterly》1993,39(1):447-453
One of the earliest applications of transfinite numbers is in the construction of derived sequences by Cantor [2]. In [6], the existence of derived sequences for countable closed sets is proved in ATR0. This existence theorem is an intermediate step in a proof that a statement concerning topological comparability is equivalent to ATR0. In actuality, the full strength of ATR0 is used in proving the existence theorem. To show this, we will derive a statement known to be equivalent to ATR0, using only RCA0 and the assertion that every countable closed set has a derived sequence. We will use three of the subsystems of second order arithmetic defined by H. Friedman ([3], [4]), which can be roughly characterized by the strength of their set comprehension axioms. RCA0 includes comprehension for Δ definable sets, ACA0 includes comprehension for arithmetical sets, and ATR0 appends to ACA0 a comprehension scheme for sets defined by transfinite recursion on arithmetical formulas. MSC: 03F35, 54B99. 相似文献
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以中国传统文化为底蕴、机械化和道理化为特色的中国传统数学,曾经取得光辉的成就.将这些思想用于计算机科学、孤子理论和量子场论,不仅可以系统地产生已有结果,还可以开辟新的研究方向,取得重大突破. 相似文献
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James H. Schmerl 《Mathematical Logic Quarterly》2010,56(5):541-548
The relationship of Grundy and chromatic numbers of graphs in the context of Reverse Mathematics is investi‐gated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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信息技术与大学数学课程整合正成为当前我国信息技术教育乃至整个教育信息化进程中的一个热点问题,探讨其整合的方式及理论基础是非常必要的.本文首先结合大学数学案例探讨了整合的三种方式:动态的课堂演示型、单机的数学实验型和全交互的网络教学型,其次探讨了整合所依据的四种理论:传播理论、建构主义理论、教学设计理论和系统理论,最后提出了自己对信息技术与大学数学课程整合的一些思考. 相似文献
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基于模糊数学和灰色理论的多层次综合评价方法及其应用 总被引:2,自引:0,他引:2
针对多层次指标体系的综合评价问题,在模糊综合评判方法的基础上,结合灰色理论,提出了一种新的定量综合评价方法—多层次模糊灰关联聚类分析综合评价方法.应用该方法对油气钻井技术进行综合评价,取得了满意的结果. 相似文献
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Jeffry L. Hirst 《Archive for Mathematical Logic》2006,45(1):1-2
This paper contains a corrected proof that the statement “every non-empty closed subset of a compact complete separable metric
space is separably closed” implies the arithmetical comprehension axiom of reverse mathematics. 相似文献
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数学建模——数学理论与应用的桥梁 总被引:3,自引:0,他引:3
成晓红 《数学的实践与认识》2001,31(5):631-632
数学建模将数学与计算机技术相结合 ,解决实际问题 ,培养学生创造、创新能力 ,提高学生综合素质 . 相似文献
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数学建模教学工程的理论与实践 总被引:7,自引:0,他引:7
王庚 《数学的实践与认识》2001,31(5):627-628
本文探讨了普通院校数学建模教学工程的理论 ,给出了一种分层次进行数学建模教育的新教学模式 (即整合模式 ) ,并介绍了安徽省安徽机电学院施行的四年三阶段的新教学模式 . 相似文献
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In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure
of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered
under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some
of these along with some other recent advances on graph minors are surveyed.
Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number
16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists
Supported in part by the Research Grant P1–0297 and by the CRC program
On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia 相似文献
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阐述了数学交流的缘起和功能 ,指出除具有一般的教学功能外 ,数学交流的教学意义特别表现在完善数学思维活动和实现数学教学的社会价值两方面 .最后 ,从三个方面探讨了数学交流观点对数学教育的启示 ,即重视培养学生的数学交流素养 ,利用师生互动的形式重塑教学过程 ,在强调认知的同时关注学生的精神生活 . 相似文献
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Geir Helleloid 《Discrete Mathematics》2009,309(8):1971-1985
In graph pegging, we view each vertex of a graph as a hole into which a peg can be placed, with checker-like “pegging moves” allowed. Motivated by well-studied questions in graph pebbling, we introduce two pegging quantities. The pegging number (respectively, the optimal pegging number) of a graph is the minimum number of pegs such that for every (respectively, some) distribution of that many pegs on the graph, any vertex can be reached by a sequence of pegging moves. We prove several basic properties of pegging and analyze the pegging number and optimal pegging number of several classes of graphs, including paths, cycles, products with complete graphs, hypercubes, and graphs of small diameter. 相似文献