Model complete theory

In model theory, a theory is called model complete if every embedding of models is an elementary equivalence.

Examples

• The theory of dense linear orders with a first and last element is complete but not model complete.
• The theory of dense linear orders with two constant symbols is model complete but not complete.

References

Chang, Chen Chung; Keisler, H. Jerome (1990) [1973], Model Theory, Studies in Logic and the Foundations of Mathematics (3rd ed.), Elsevier, ISBN 978-0-444-88054-3