Scott-Karp analysis without sentences
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910015389958144 |
|---|---|
| author | Brunner, Andreas Morgan, Charles Pinto, Darllan Concieção |
| author_facet | Brunner, Andreas Morgan, Charles Pinto, Darllan Concieção |
| contents | Scott and Karp gave an analysis which provides a level-by-level equivalence between global similarity between two structures and local commonality in terms of sharing particular invariants. Scott and Karp's local invariants were certain infinitary formulae.
We give a more abstract version of the local side of Scott-Karp analysis which avoids the use of infinitary languages. We show the resulting hierarchies are still provide desired equivalences in the classical setting.
Moreover, the abstract nature of our analysis, as we show, makes it suitable to provide local level-by-level equivalents to Hjorth's much more general version of global similarity in the context of topological group actions on topological groups.
We, furthermore, provide, analogously to the classical work of Ehrenfeucht and Fraïssé, novel game theoretic equivalents for Hjorth's global similarity relations and some natural variants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scott-Karp analysis without sentences Brunner, Andreas Morgan, Charles Pinto, Darllan Concieção Logic 03C10 Scott and Karp gave an analysis which provides a level-by-level equivalence between global similarity between two structures and local commonality in terms of sharing particular invariants. Scott and Karp's local invariants were certain infinitary formulae. We give a more abstract version of the local side of Scott-Karp analysis which avoids the use of infinitary languages. We show the resulting hierarchies are still provide desired equivalences in the classical setting. Moreover, the abstract nature of our analysis, as we show, makes it suitable to provide local level-by-level equivalents to Hjorth's much more general version of global similarity in the context of topological group actions on topological groups. We, furthermore, provide, analogously to the classical work of Ehrenfeucht and Fraïssé, novel game theoretic equivalents for Hjorth's global similarity relations and some natural variants. |
| title | Scott-Karp analysis without sentences |
| topic | Logic 03C10 |
| url | https://arxiv.org/abs/2602.07646 |