scholarly journals Using Ultrafilters to Prove Ramsey-type Theorems

David J. Fernández-Bretón
1996 ◽  
Vol 150 (1-3) ◽  
pp. 61-67 ◽  
Miklós Bóna ◽  
Géza Tóth

2012 ◽  
Vol 77 (4) ◽  
pp. 1272-1280 ◽  
Stephen Flood

AbstractIn this paper, we propose a weak regularity principle which is similar to both weak König's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.

10.37236/8385 ◽  
2019 ◽  
Vol 26 (3) ◽  
Eben Blaisdell ◽  
András Gyárfás ◽  
Robert A. Krueger ◽  
Ronen Wdowinski

We show that for $n \geq 3, n\ne 5$, in any partition of $\mathcal{P}(n)$, the set of all subsets of $[n]=\{1,2,\dots,n\}$, into $2^{n-2}-1$ parts, some part must contain a triangle — three different subsets $A,B,C\subseteq [n]$ such that $A\cap B,A\cap C,B\cap C$ have distinct representatives. This is sharp, since by placing two complementary pairs of sets into each partition class, we have a partition into $2^{n-2}$ triangle-free parts.  We also address a more general Ramsey-type problem: for a given graph $G$, find (estimate) $f(n,G)$, the smallest number of colors needed for a coloring of $\mathcal{P}(n)$, such that no color class contains a Berge-$G$ subhypergraph. We give an upper bound for $f(n,G)$ for any connected graph $G$ which is asymptotically sharp when $G$ is a cycle, path, or star. Additional bounds are given when $G$ is a $4$-cycle and when $G$ is a claw.

2008 ◽  
Vol 9 (2) ◽  
pp. 135-159 ◽  
Erkki Koskela ◽  
Leopold von Thadden

Abstract We consider the issue of steady-state optimal factor taxation in a Ramsey-type dynamic general equilibrium setting with two distinct distortions: (i) taxes on capital and labour are the only available tax instruments for raising revenues and (ii) labour markets are subject to an inefficiency resulting from wage bargaining. If considered in isolation, the two distortions create conflicting demands on the wage tax, while calling for a zero capital tax. By combining the two distortions, we arrive at the conclusion that both instruments should be used, implying that the zero capital tax result in general is no longer valid under imperfectly competitive labour markets.

1985 ◽  
Vol 27 ◽  
pp. 5-10
S. A. Burr ◽  
P. Erdös

Let A be a sequence of positive integers. Define P(A) to be the set of all integers representable as a sum of distinct terms of A. Note that if A contains a repeated value, we are free to use it as many times as it occurs in A. We call A complete if every sufficiently large positive integer is in P(A), and entirely complete if every positive integer is in P(A). Completeness properties have received considerable, if somewhat sporadic, attention over the years. See Chapter 6 of [3] for a survey.

1997 ◽  
Vol 78 (21) ◽  
pp. 4023-4026 ◽  
Frank Sander ◽  
Thibaut Devolder ◽  
Tilman Esslinger ◽  
Theodor W. Hänsch

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