Transformations of the transfinite plane

Abstract We study the existence of transformations transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for cardinals. To exemplify: we prove every inaccessible cardinal $\kappa $ , if admits a stationary set does not reflect at inaccessibles, then negative relation \nrightarrow [\kappa ]^2_\kappa implies group $(G,+)$ size there exists map $f:G\rightarrow G$ such $X\subseteq and $g\in exist $x\neq y$ in X $f(x+y)=g$ .