View source for Elementary equivalence

{{TEX|done}}{{MSC|03C07}}

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}}