论文标题
单色指数三元组：超滤波器证明
Monochromatic exponential triples: an ultrafilter proof
论文作者
论文摘要
我们提供了简短的超滤波器证明单色指数三元组的存在$ \ {a，b，b，b^a \} $在自然数的任何有限颜色中。证明是从头开始给出的，仅使用拉姆齐定理，渐近密度的概念以及将超级滤波器作为先决条件的定义。然后，我们使用特殊的超级滤术概括了构造，该超滤波器的存在在Ultrafters的代数中是众所周知的，并证明了无限单色指数模式的新结果。
We present a short ultrafilter proof of the existence of monochromatic exponential triples $\{a, b, b^a\}$ in any finite coloring of the natural numbers. The proof is given from scratch and uses only Ramsey's theorem, the notion of asymptotic density and the definition of ultrafilter as prerequisites. We then generalize the construction using a special ultrafilter whose existence is well known in the algebra of ultrafilters, and prove a new result on the existence of infinite monochromatic exponential patterns.
