Positive indiscernibles
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913351809892352 |
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| author | Kamsma, Mark |
| author_facet | Kamsma, Mark |
| contents | We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$_0$-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing -- rather than locally basing or EM-basing -- str-trees on s-trees and str$_0$-trees on str-trees. As an application we show that a thick positive theory has $k$-TP$_2$ iff it has $2$-TP$_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14127 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Positive indiscernibles Kamsma, Mark Logic 03C45 (Primary), 03C95, 03B20 (Secondary) We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$_0$-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing -- rather than locally basing or EM-basing -- str-trees on s-trees and str$_0$-trees on str-trees. As an application we show that a thick positive theory has $k$-TP$_2$ iff it has $2$-TP$_2$. |
| title | Positive indiscernibles |
| topic | Logic 03C45 (Primary), 03C95, 03B20 (Secondary) |
| url | https://arxiv.org/abs/2305.14127 |