# Elementary equivalence

From Encyclopedia of Mathematics

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

**How to Cite This Entry:**

Elementary equivalence.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Elementary_equivalence&oldid=54592