Relative categoricity in abelian groups. II

DOI10.1016/J.APAL.2008.03.007zbMath1163.03018OpenAlexW2075614966MaRDI QIDQ1012332

Wilfrid Hodges, Anatoly V. Yakovlev

Publication date: 16 April 2009

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2008.03.007

zbMATH Keywords

abelian groupsmodel theoryrelative categoricitygroup pairs

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Abelian groups (20K99) Categoricity and completeness of theories (03C35)

Cites Work

• Categoricity over P for first order T or categoricity for \(\phi\) \(\in {\mathcal L}_{\omega_ 1\omega}\) can stop at \(\aleph_ k\) while holding for \(\aleph_ 0,\dots ,\aleph_{k-1}\)
• Classification theory over a predicate. I
• Classification theory and the number of non-isomorphic models.
• Abelian groups \(\aleph_ 0\)-categorical over a subgroup
• Automorphisms of Bounded Abelian Groups
• Categoricity in Power
• On $ω_1$-categorical theories of abelian groups
• The elementary theory of abelian groups
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