Elementary equivalence

2020 Mathematics Subject Classification: Primary: 03C07 [MSN][ZBL]

The relationship between models for a first-order language $L$ for which the sentences of $L$ have the same truth values in the models. Such models are said to be "elementarily equivalent" or "first-order equivalent".

See:

• Fraïssé characterization of elementary equivalence
• Keisler-Shelah isomorphism theorem
• Abstract algebraic logic

References

• Hodges, Wilfrid. "Model theory" Encyclopaedia of Mathematics and Its Applications 42. Cambridge University Press (2008) ISBN 978-0-521-06636-5 Zbl 1139.03021