Transformations of the transfinite plane
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Abstract We study the existence of transformations of the transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for uncountable cardinals. To exemplify: we prove that for every inaccessible cardinal $\kappa $ , if $\kappa $ admits a stationary set that does not reflect at inaccessibles, then the classical negative partition relation $\kappa \nrightarrow [\kappa ]^2_\kappa $ implies that for every Abelian group $(G,+)$ of size $\kappa $ , there exists a map $f:G\rightarrow G$ such that for every $X\subseteq G$ of size $\kappa $ and every $g\in G$ , there exist $x\neq y$ in X such that $f(x+y)=g$ .
2001 ◽
Vol 37
(1-2)
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pp. 233-236
1995 ◽
Vol 44
(2)
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pp. 395-402
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2011 ◽
Vol 10
(03)
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pp. 377-389
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2017 ◽
Vol 16
(10)
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pp. 1750200
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1981 ◽
Vol 90
(2)
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pp. 273-278
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2018 ◽
Vol 167
(02)
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pp. 229-247
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