论文标题
Hindman定理的回归版本
Regressive versions of Hindman's Theorem
论文作者
论文摘要
当ErdőS和Rado的规范Ramsey定理应用于回归函数时，人们通过Kanamori和McAloon获得了回归性Ramsey定理。泰勒（Taylor）被证明是欣德曼（Hindman）定理的“规范”版本，类似于规范的拉姆齐（Ramsey）定理。我们介绍了泰勒（Taylor）规范的Hindman定理限制回归功能的子类，即$λ$回归功能，相对于Min-Anolomenione的适当版本，并证明了这种回归性Hindman定理和其自然限制的反向数学的结果。 特别是我们证明，对原理的第一个非平凡限制等同于算术理解。此外，我们证明，相同的原理可以强烈减少基础$ω$ oppontions的顺序良好的保存原则。
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 $λ$-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 this same principle strongly computably reduces the well-ordering-preservation principle for base-$ω$ exponentiation.
