A variety of partially conservative sentences
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912191623462912 |
|---|---|
| author | Kogure, Haruka Kurahashi, Taishi |
| author_facet | Kogure, Haruka Kurahashi, Taishi |
| contents | We study the existence of a $Θ$ sentence which is simultaneously $Γ$-conservative over consistent RE extensions $T$ and $U$ of Peano Arithmetic for various reasonable pairs $(Γ, Θ)$. As a result of this study, we prove the existence of a sentence which is essentially $Θ$ and exactly hereditarily $Γ$-conservative over any single theory $T$ for various reasonable pairs $(Γ, Θ)$. This is an affirmative answer to Guaspari's question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A variety of partially conservative sentences Kogure, Haruka Kurahashi, Taishi Logic We study the existence of a $Θ$ sentence which is simultaneously $Γ$-conservative over consistent RE extensions $T$ and $U$ of Peano Arithmetic for various reasonable pairs $(Γ, Θ)$. As a result of this study, we prove the existence of a sentence which is essentially $Θ$ and exactly hereditarily $Γ$-conservative over any single theory $T$ for various reasonable pairs $(Γ, Θ)$. This is an affirmative answer to Guaspari's question. |
| title | A variety of partially conservative sentences |
| topic | Logic |
| url | https://arxiv.org/abs/2412.08208 |