• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1001-1011
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• 2018

We introduce some variants of the finite Ramsey theorem. The variants are based on a refinement of homogeneity. In particular, they cover homogeneity, minimal homogeneity, end-homogeneity as special cases. We also show how to obtain upper bounds for the corresponding Ramsey numbers.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.709-721
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• 2005

G. Gruenhage gave a characterization of paracompactness of locally compact spaces in terms of game theory ([6]). Starting from that result we give another such characterization using a selective version of that game, and study a selection principle in the class of locally compact spaces and its relationships with game theory and a Ramseyan partition relation. We also consider a selective version of paracompactness.

• Journal of the Korean Institute of Gas
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• v.2 no.3
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• pp.18-24
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• 1998

This paper attempts to improve domestic natural gas pricing system, thereby optimizing social welfare. This is done by deriving theoretical frameworks of natural gas pricing, which make use of both Ramsey component pricing rule and Efficient component pricing rule based on the theory of marginal cost. Allocative efficiency and social welfare between gas prices derived from the three pricing mechanism, present Cost-based pricing, Ramsey component pricing rule and Efficient component pricing rule, are analysed and compared in the case study. For the city gas, allocative efficiency of Cost-based pricing is higher than that of Ramsey component pricing rule and Efficient component pricing rule. In contrast, for the natural gas consumed for power generation, allocative efficiency of Cost-based pricing is lower than the other two pricing systems. It also turns out that social welfare is improved by the prices driven from Ramsey component pricing rule and Efficient component pricing rule rather than present Cost-based pricing.

• Korean Journal of Logic
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• v.17 no.1
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• pp.1-32
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• 2014

Both 5.52 and 5.521 of the Tractatus Logico-Philosophicus raise several questions. In this paper I will explicate Wittgenstein's concept of generality by answering such questions. These questions and problems are closely intertwined. I will try to show what follows. It is ${\xi}$-conditions that are most decisive on the concept of generality of the Tractatus. Except Ramsey, commentators such as Anscombe, Glock, Kenny etc. failed in accurately grasping the Wittgenstein's thoughts concerning ${\xi}$-condition and their claims are not fair at all. Futhermore, from a view point of history of logic, 5.52 has very important significances. That is to say, it anticipates for the first time a possibility of infinitary logic and the concept of universe of discourse in model theory.

• Korean Journal of Logic
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• v.20 no.1
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• pp.69-96
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• 2017

Wittgenstein criticizes explicitly Russell's theory of types and, in particular, his axiom of reducibility in the Tractatus Logico-Philosophicus. What, then, is the point of Wittgenstein's criticisms of Russell's theory of types? As a preliminary study to answer this question, I will examine how Wittgenstein criticized Russell's axiom of reducibility. Wittgenstein declares that Russell's axiom of reducibility is not a logical proposition, that if it is true it will be so mere by a happy chance and that "we can imagine a world in which the axiom of reducibility is not valid." What, then, is the ground for that? I will endeavor to show that by explicating the ideas of Wittgenstein's 1913 letter to Russell, those ideas decisively influenced on Ramsey's and Waismann's model which intended to show that the axiom of reducibility is not valid.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.101-112
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• 2005

In this article, we introduce a generous but eccentric genius in mathematics, Paul Erdos. He invented probabilistic methods, pioneered in their applications to discrete mathematics, and estabilshed new theories, which are regarded as the greatest among his contributions to mathematical world. Here we introduce the probabilistic methods and random graph theory developed by Erdos and look at his life in glance with great respect for him.

• Environmental and Resource Economics Review
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• v.23 no.2
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• pp.225-248
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• 2014

The purpose of this study is to estimate the optimal tax rate for gasoline in Korea, by utilizing both the parameters for the estimation of the optimal fuel taxes and the theoretical model considering externalities proposed by Parry and Small (2005). The result of simulation shows that the optimum fuel taxes in Korea is calculated in 382 korean won per liter, which is lower than fuel tax rate(529 korean won per liter) currently being imposed. The fuel tax is composed of two types of tax. First is Pigouvian tax caused by negative externality such as traffic congestion and accidents etc. And second is Ramsey tax for optimal commodity sales taxes. We find that Pigouvian tax in Korea is higher than one of U.S. and U.K and Ramsey tax is very small due to the inelastic labor supply comparing to consumption elasticity of fuel. When adjusting the elasticity of labor supply to the UK level, the optimal fuel tax in Korea is very close to the current level of 480 korean won per liter. This paper contributes to suggest the reasonable estimation and discussion in the social optimum fuel tax rates by utilizing the theory and simulation and improve the possibility of the derivation of optimum fuel taxes through both securing the exact parameters and modifying the theoretical model suitable for Korea.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.379-389
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• 2020

An r-color Rado number N = R(𝓛, r) for a system 𝓛 of equations is the least integer, provided it exists, such that for every r-coloring of the set {1, 2, …, N}, there is a monochromatic solution to 𝓛. In this paper, we study the 2-color Rado number R(𝓔, 2) for 𝓔 : x₁ + x₂ + ⋯ + x_n = y₁ + y₂ = z when n ≥ 4.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1341-1354
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• 2021

Let r ≥ 2, and let k_i ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k₁, k₂, k₃, …, k_r; r) such that for any n ≥ w, every r-colouring of [1, n] admits a k_i-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w₂(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w₂(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w₂(k; r) for 2 ≤ r ≤ k.

• Journal of Korean Philosophical Society
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• v.116
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• pp.133-154
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• 2010

Eliminativist about mentality want to throw out propositional attitude. In this respect, according to R. G. Swinburne, Lynne R. Baker, this theory seems to be self refuting. But it is not so clear enough in what sense eliminativism is self refuting. There are several construals of self-refutation argument against eliminativism. Among them, Patricia Churchland's simple version is defended here. For doing this, we need to analyze William Ramsey's reconstruction of self- refutation argument and J. L. Mackie's famous concept of self-refutation. As a result of this analysis, we can understand most self-refutation arguments against eliminativism don't succeed to defeat eliminativism with this argument.