Abstract
Let TFAG be the theory of torsion-free abelian groups. We show that if there is no countable transitive model of ZFC- + "R(ω) exists", then TFAG is aΔ12- complete; in particular, this is consistent with ZFC. We define the α-ary Schröder- Bernstein property, and show that TFAG fails the α-ary Schröder-Bernstein property for every α < R (ω). We leave open whether or not TFAG can have the R(ω)-ary Schröder- Bernstein property; if it did, then it would not be aΔ12 -complete, and hence not Borel complete.
Original language | English |
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Pages (from-to) | 275-297 |
Number of pages | 23 |
Journal | Fundamenta Mathematicae |
Volume | 247 |
Issue number | 3 |
DOIs | |
State | Published - 2019 |
Bibliographical note
Publisher Copyright:© Instytut Matematyczny PAN, 2019.
Keywords
- Borel complexity
- Torsion-free abelian groups