Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914629845778432 |
|---|---|
| author | Fernández-Duque, David Weiermann, Andreas |
| author_facet | Fernández-Duque, David Weiermann, Andreas |
| contents | We prove that Buchholz's system of fundamental sequences for the $\vartheta$ function enjoys various regularity conditions, including the Bachmann property. We partially extend these results to variants of the $\vartheta$ function, including a version without addition for countable ordinals. We conclude that the Hardy functions based on these notation systems enjoy natural monotonicity properties and majorize all functions defined by primitive recursion along $\vartheta(\varepsilon_{Ω+1})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_07758 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal Fernández-Duque, David Weiermann, Andreas Logic We prove that Buchholz's system of fundamental sequences for the $\vartheta$ function enjoys various regularity conditions, including the Bachmann property. We partially extend these results to variants of the $\vartheta$ function, including a version without addition for countable ordinals. We conclude that the Hardy functions based on these notation systems enjoy natural monotonicity properties and majorize all functions defined by primitive recursion along $\vartheta(\varepsilon_{Ω+1})$. |
| title | Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal |
| topic | Logic |
| url | https://arxiv.org/abs/2203.07758 |