Smullyan's truth and provability
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929679274868736 |
|---|---|
| author | Kurahashi, Taishi Tominaga, Kohei |
| author_facet | Kurahashi, Taishi Tominaga, Kohei |
| contents | We revisit Smullyan's paper ``Truth and Provability'' (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan's framework discussed in that paper. Second, we clarify the relationship between three theorems proved by Smullyan and other newly introduced properties for Smullyan models in terms of both implications and non-implications. Third, we construct two Smullyan models based on arithmetical ideas and show the correspondence between the properties of these Smullyan models and those concerning truth and provability in arithmetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smullyan's truth and provability Kurahashi, Taishi Tominaga, Kohei Logic We revisit Smullyan's paper ``Truth and Provability'' (2013) for three purposes. First, we introduce the notion of Smullyan models to give a precise definition for Smullyan's framework discussed in that paper. Second, we clarify the relationship between three theorems proved by Smullyan and other newly introduced properties for Smullyan models in terms of both implications and non-implications. Third, we construct two Smullyan models based on arithmetical ideas and show the correspondence between the properties of these Smullyan models and those concerning truth and provability in arithmetic. |
| title | Smullyan's truth and provability |
| topic | Logic |
| url | https://arxiv.org/abs/2410.17895 |