When the Canonical Ramsey’s Theorem by Erdős and Rado is applied to regressive functions, one obtains the Regressive Ramsey’s Theorem by Kanamori and McAloon. Taylor proved a “canonical” version of Hindman’s Theorem, analogous to the Canonical Ramsey’s Theorem. We introduce the restriction of Taylor’s Canonical Hindman’s Theorem to a subclass of the regressive functions, the \(\lambda \)-regressive functions, relative to an adequate version of min-homogeneity and prove some results about the Reverse Mathematics of this Regressive Hindman’s Theorem and of natural restrictions of it. In particular we prove that the first non-trivial restriction of the principle is equivalent to Arithmetical Comprehension. We furthermore prove that the well-ordering-preservation principle for base-\(\omega \) exponentiation is reducible to this same principle by a uniform computable reduction.

当 Erdős 和 Rado 的规范拉姆齐定理应用于回归函数时，我们得到 Kanamori 和 McAloon 的回归拉姆齐定理。泰勒证明了辛德曼定理的“规范”版本，类似于规范拉姆齐定理。我们将泰勒正则 Hindman 定理的限制引入到回归函数的子类，即\(\lambda \)回归函数，相对于最小同质性的适当版本，并证明了有关该回归 Hindman 定理的逆向数学的一些结果以及它的自然限制。特别是，我们证明了该原理的第一个非平凡限制相当于算术理解。我们进一步证明，基数\(\omega \)求幂的良好排序保留原理可以通过统一可计算约简简化为相同的原理。