In Paolini and Shelah (2024), we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper, we show that our construction from Paolini and Shelah (2024) satisfies several additional properties of interest. We deduce from this that countable torsion-free abelian groups are faithfully Borel complete; in fact, more strongly, we can -interpret countable graphs in them. Secondly, we show that the relation of pure embeddability (i.e., elementary embeddability) among countable models of Th(ℤ(ω)) is a complete analytic quasi-order.
Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order
Paolini G.
;
2025-01-01
Abstract
In Paolini and Shelah (2024), we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper, we show that our construction from Paolini and Shelah (2024) satisfies several additional properties of interest. We deduce from this that countable torsion-free abelian groups are faithfully Borel complete; in fact, more strongly, we can -interpret countable graphs in them. Secondly, we show that the relation of pure embeddability (i.e., elementary embeddability) among countable models of Th(ℤ(ω)) is a complete analytic quasi-order.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
