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- Title
Regressive versions of Hindman's theorem.
- Authors
Carlucci, Lorenzo; Mainardi, Leonardo
- Abstract
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 the well-ordering-preservation principle for base- ω exponentiation is reducible to this same principle by a uniform computable reduction.
- Subjects
REVERSE mathematics; EXPONENTIATION; RAMSEY theory
- Publication
Archive for Mathematical Logic, 2024, Vol 63, Issue 3/4, p447
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-023-00901-6