COUNTING SIBLINGS IN UNIVERSAL THEORIES
We show that if a countable structure M in a finite relational language is not cellular, then there is an age-preserving $N \supseteq M$ such that $2^{\aleph _0}$ many structures are bi-embeddable with N. The proof proceeds by a case division based on mutual algebraicity.
Gespeichert in:
| Veröffentlicht in: | The Journal of symbolic logic 2022-09, Vol.87 (3), p.1130-1155 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | We show that if a countable structure M in a finite relational language is not cellular, then there is an age-preserving
$N \supseteq M$
such that
$2^{\aleph _0}$
many structures are bi-embeddable with N. The proof proceeds by a case division based on mutual algebraicity. |
|---|---|
| ISSN: | 0022-4812 1943-5886 |
| DOI: | 10.1017/jsl.2022.3 |