Ramsey's witnesses
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914337854062592 |
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| author | Di Nasso, Mauro Baglini, Lorenzo Luperi Mamino, Marcello Mennuni, Rosario Ragosta, Mariaclara |
| author_facet | Di Nasso, Mauro Baglini, Lorenzo Luperi Mamino, Marcello Mennuni, Rosario Ragosta, Mariaclara |
| contents | We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products and dubbed Ramsey's witnesses; and we also consider their nonstandard counterparts as pairs of hypernatural numbers, called Ramsey pairs. These characterisations are then used to determine whether various configurations involving polynomials and exponentials are Ramsey partition regular over the natural numbers. In particular, this provides negative answers to several questions recently posed by Kra, Moreira, Richter and Robertson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ramsey's witnesses Di Nasso, Mauro Baglini, Lorenzo Luperi Mamino, Marcello Mennuni, Rosario Ragosta, Mariaclara Logic Combinatorics 05D10 (Primary) 26E35, 03H15, 11U10, 05A17, 54D80 (Secondary) We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products and dubbed Ramsey's witnesses; and we also consider their nonstandard counterparts as pairs of hypernatural numbers, called Ramsey pairs. These characterisations are then used to determine whether various configurations involving polynomials and exponentials are Ramsey partition regular over the natural numbers. In particular, this provides negative answers to several questions recently posed by Kra, Moreira, Richter and Robertson. |
| title | Ramsey's witnesses |
| topic | Logic Combinatorics 05D10 (Primary) 26E35, 03H15, 11U10, 05A17, 54D80 (Secondary) |
| url | https://arxiv.org/abs/2503.09246 |